TILDA Swinton is standing on the beach at Nairn, the beige sand dotted with worm-casts, bladder-wrack and mussel shells the shape and colour of bruised eyes. She is wearing a fuzzy orange coat, her red hair is dyed blonde, and she is being photographed with her back to the Moray Firth. Swinton has called this Highland town home for seven years – a point of stasis in a life characterised by flux. Her film commitments mean she is always just back from a string of foreign cities, and always on the point of leaving for more. Today she is jetlagged, having not long returned from New York, Berlin, Paris and Los Angeles; she spent her 48th birthday, Bonfire Night, attending an American Film Institute tribute to her work. Two days after this interview she is off to London, Chile, Mexico and Los Angeles once more.
It is a crazy way to live, almost literally maddening. When she comes back home to her 11-year-old twins, Honor and Xavier, and their father, the painter and playwright John Byrne, "It's like that scene in Oliver! when he wakes up in the grandfather's house and he looks out of the window and sings, 'Who will buy this wonderful morning?' and all these milkmaids come past with yokes on their shoulders and brass bands strike up. It really is like that. When I get to Inverness airport, I get off the plane and I want to kiss the tarmac."
Swinton loves Nairn, and thinks it natural that a movie star should set up home here. As we walk back to her house, she points out that Charlie Chaplin used to holiday in the town, that Margaret Rutherford stayed here while suffering from "lovesickness" and that Basil Rathbone shot one of his Sherlock Holmes adventures at the local railway station.
The way Swinton looks (serious, imperious, mysterious) can belie the way she really is (whimsical, childish in a good way, sporadically daft). It's as if a character from the Beano suddenly fetched up in the pages of Vogue. In the kitchen we are joined for a bite to eat – it is the sort of place where there always seems to be soup or scones on the go – by Byrne, resplendent in a Harris tweed waistcoat, who is taking a break from adapting The Cherry Orchard for Edinburgh's Royal Lyceum.
Byrne and Swinton have been in the papers a lot this year after it emerged that both were in new relationships. Yet seeing them together it is clear there is no acrimony. She mentions her new partner, the 30-year-old painter Sandro Kopp, in front of him, provoking no reaction whatsoever; it's clearly not a difficult subject. In fact, she and Byrne, who is 68, seem rather like a comedy double act – Pale and Interesting. She speaks in a cut-glass, high-class English accent; his Paisley tones are muffled by his estimable moustache.
They tell each other silly jokes, and Swinton recalls some of their more juvenile antics. "They're so sick of me in the butcher's," she says, "going in and asking if I can have a mince round." She turns to Byrne. "Do you remember when we went into that fabric shop in Elgin and asked if you could get felt in there? I don't think the woman knew what we were giggling about."
I first met Tilda Swinton in the summer of 2001 when she was still living in Easter Ross. Back then she was best known for her work with the late avant-garde director Derek Jarman, but was beginning to build her profile with a series of supporting roles in American films including Vanilla Sky and Adaptation. Her ascendancy reached its zenith with her appearance as the White Witch in The Lion, The Witch And The Wardrobe, and this year's Oscar for Michael Clayton. Her increasing fame has been "kind of great, to be honest. I'm happy to be a movie star. The downside of being an arthouse freak is that it's a kind of elitist sport. I really like people waving at me in airports."
This year, though, she has been under intense scrutiny as a result of her relationship with Kopp, whom she met on the set of the Narnia film. What has that been like? She munches a cracker and considers. "Nothing has changed for us. It's just this swarm has come over. We've been happily living our lives for four or five years in this configuration. Then when I won a Bafta I became interesting to a certain kind of press who couldn't have cared less about me 24 hours earlier because I was, y'know, The Freak."
Swinton says she takes great pleasure in the idea of openness, and would like it known that her home is "a shame-free zone". The media stooshie around her lifestyle reminds me of the way Derek Jarman, in his candour about being gay and HIV Positive, became a tabloid bte noire.
"Well, the similarity is we don't care," Swinton nods. "It's like a bunch of kids from another school laughing about you. It's not ever going to affect us. Of course, one's concerned about the children, but fortunately we feel that our children are immune, partly because they've lived with us all for almost half their lives, and so for them there is nothing remotely exotic and weird about it."
In any case, she says, it's all terribly simple. "There has been this idea given out that we're in this complete debauch in this house. Well, that is a fabulous fantasy. It really is very straightforward. You're talking about a couple having children, becoming not a couple any more but remaining the parents of children, and having other coupledoms with other people. It's about consecutive relationships not concurrent relationships. We're not all sleeping together, I'm sorry to tell you." She laughs. "It's so much more boring than that."
Confusingly, the situation was reported widely as a mnage trois. "But that's because there was no announcement of a break-up. There is no break-up. There's been an evolution over a long time which we didn't go running to the newspapers with because, frankly, there are other things going on in the world that deserve the space. And we are private people, and these evolutions go on in every single family. We just breathed our way through it and we've come to feel very good about it all." The whole idea of jealousy is completely alien to her.
What's Sandro like? "He's fantastic. He would be here today if he wasn't in New York. He was born in Germany, and has a German father and New Zealandish mother. He left Germany when he was 20 and was living in New Zealand when I met him. He's an extraordinary person. Very funny and wise and a dude." She laughs. "He's a sweetheart, a pretty switched-on individual, and a very interesting figurative painter." She tells me later that Kopp's grandfather was a leading physicist in Nazi Germany.
I mention that I had gone on to Kopp's website and seen a painting he had made of Swinton. "He's constantly trying to paint me," she says. "In all the paintings I'm absolutely exhausted because he always wants to paint me when I've just put two children to bed. So I'm always slightly falling asleep and looking like that in his paintings."
Does he stay here? "He comes and goes. We have this strange existence. He and I live together when I'm on the road, but I'm on the road quite a bit. We don't have a place together, but we do have a variety of cities that we end up in pretty regularly. We have a way of living in New York, LA, Paris, Berlin, Rome and Milan. Our way of living that has various ingredients in it, including a fantastic card game called Shithead which we play pretty much all the time. If we are sitting in a hotel or by an airport gate, we crack open the cards and play Shithead. That's our equivalent of a fireside."
Earlier, I had asked how she maintained a sense of calm and continuity while jetting around the world. Now, with reference to Kopp, she returns to this subject. "I met Sandro four years ago, and there was a point three years before that when John, very sweetly, said to me, 'I'm not coming on the road any more. I can't do it.' Because he'd noticed, poor thing, that he never got any work done when he was with me. So we agreed that I would go by myself, either with the children or without them. And God it was lonely. It really was. So it was an amazing stroke of luck to meet this fellow traveller."
We move through to the drawing room. It's a fairly large but cosy space decorated with paintings by Byrne and others, including his portrait of the writer AL Kennedy who recently came to visit with her collection of Doctor Who DVDs. There's a piano on which Xavier can play 'Stairway To Heaven', and an open fire on which Swinton deposits the first bag of peat of the year. She walks over to the iPod and chooses music. Patti Smith starts singing "Jesus died for somebody's sins but not mine" but then Swinton changes her mind and switches to Kate Bush. She sits on a flowery sofa, legs outstretched, balances my voice recorder on her stomach so Rosie the springer spaniel doesn't disturb it, and continues to talk.
A lot of our discussion both today and when I last came to Nairn two months ago is taken up with her upbringing. Despite that accent, which she describes as "something out of the bloody 1930s BBC", Swinton is Scottish. Her land-owning family can trace their roots back to the 9th century. The estate is Kimmerghame in Berwickshire, and Swinton grew up in the big house there, on and off. Her father, Major-General Sir John Swinton, inherited when his father died in 1972.
They are a military family. Tilda's younger brother William has commanded the Scots Guards, as his father and grandfather did before him. As the daughter of a soldier, she moved around a lot during her early years, living on military bases in Germany and at Sandhurst military academy. She remembers being about three and standing on the parade ground at Sandhurst and feeling very safe. She thinks, looking back, that she understood that it was a kind of ritual space, a place where people performed, and believes this was a very early flash of how she would later feel in front of the camera – at peace and in control.
Another key moment in her development as an actor – not that she likes that word – came when she was 10 years old and sent from Scotland to West Heath boarding school in Kent. She was on the train, feeling absolutely miserable, and she suddenly realised – with pleasure – that no one else in the carriage could possibly know how she felt inside. There was a gap between what was in her heart and what was on her face. That moment was the first realisation that being a cinema performer was something she could do. That was interesting because it was also the first time that she had a sense of how she could carve out a life of her own. She had three brothers and always felt rather overlooked.
"It was very clear," she says, "that the boys in the family had a life laid out for them that was pretty well worn, set up, established and honoured. It involved all sorts of ritualistic things like learning to shoot and all going to the same school as their father, grandfather and great-grandfather. It felt like it would have been more convenient for me to be a boy, and it did definitely look like they were having more fun."
Swinton felt marginalised because of her gender, and misunderstood because she felt early on that she was some kind of artist, but "most of the things I was interested in were anathema to my family. They are singularly philistine when it comes to art."
Then there was the way she looked. She has always been striking, but it's a look that is perhaps more appreciated in a film star and fashion muse than in a little girl. I ask when she first become aware that she had something about her appearance that set her apart from other people.
"Well, I was always aware that I wasn't pretty," she says, "which I think is a great advantage. I don't think it's something to be wished on your child – that they be pretty – because it's an easy currency that can get spent too quickly. Friends of mine who were pretty, who had a regularness about them, got caught up in all sorts of trafficking of their own prettiness. Even pre-sexual, there would be this knowledge that they were blonde, blue-eyed, bow-lipped and that was expected of them. It was a pressure. And I was aware that I didn't have that, and so I was under wraps and I didn't really qualify as a girl for that reason.
"I never really felt girly. I was brought up in a very male-orientated family, by a very feminine mother, but I didn't have much access to her. Maybe if I hadn't gone to boarding school, if I had been in the same house as her when I was between 10 and 17 then I might have had more access to girliness via her. But I didn't. And so I just opted out of any sexuality and found that a really safe, really strong place to be."
There was no sense of missing out? "No. The only thing that I still have no sense of humour about is that at boarding school – and I forgive my upbringing everything but this – we were not allowed any music. I think that's a gross abuse of a young person, particularly a teenager during the Punk era. I suppose it was some clever way of keeping us away from sex or something, but it really sucked."
She is still very proud that, even though she had no way of playing it, she managed to acquire a copy of David Bowie's Aladdin Sane. She bought it for the front cover, having noticed a resemblance between them. "Yeah, I always looked like him," she says. "And the fact that he not only looked physically like me specifically, but was also of indeterminate gender was really striking, and it felt like good company."
Has she ever met him? "Do you know, the awful thing is that I stood behind him in New York a month ago. We were both at an event. And I was virtually dressed up as him as well. My look that night was completely Ziggy. And I just couldn't speak to him. I'm very shy about Bowie."
She was less shy around pop stars on the night of the Oscars in February when she won an Academy Award as best supporting actress for her work in Michael Clayton. The ceremony itself is a blur. She was chatting to George Clooney and the Coen Brothers and the next thing her name was read out, "and I just remember this feeling of horror and I can't remember much after that". Afterwards, she went to a party at Prince's house and she introduced herself to Stevie Wonder and danced when he played "Superstition."
It's time to pick up the children. Rosie and I climb in the front passenger seat of Swinton's Fiat, CDs by Love and Nick Cave spilling from the glove compartment. "Welcome to the Wicker Man!" says Swinton when we pull up outside the school, which is set in the woods.
Honor and Xavier are playing on tree swings, but she tempts them into the car with the promise of ginger cakes, and we drive back to Nairn, talking about Honor's pet hare, Gentle. It's obvious that Swinton has an incredibly close relationship with her children and that they enjoy each other's company. Aware that children often rebel against the lifestyle of their parents, she jokes that hers might grow up to be "Nazi accountants".
Back in the house, Johnny Cash on the iPod, I ask about Jarman. Swinton has never been at ease with her background as one of the "owning classes", and spent a good number of years seeking a way of life and work that had nothing to do with elitism and inheritance. After school, she spent a year volunteering in a children's home in a black township in South Africa. She then studied social and political science and English literature at Cambridge University. On graduation she worked rather half-heartedly as a stage actress, including a "boring" period with the Royal Shakespeare Company. Then in 1985 she met Jarman and became part of his misfit troupe. They made a lot of work together, beginning with Caravaggio, her first film if you don't count the vampire movie she shot in Cambridge, in 1986.
It was significant for Swinton that she and Jarman had similar backgrounds in posh military families. It taught her that you could come from that and still "go through the looking-glass" to become an artist. Was he, then, a father figure?
"A godfather figure," she replies. "He wasn't remotely fatherly, but he was a mentor of sorts, and very protective of me. If I had never met Derek Jarman I don't see how I could have been a performer. I was not interested in the theatre, and when I was first making films there was nothing. There was Richard Attenborough and Merchant-Ivory and Alan Parker." She pronounces these names with obvious distaste.
"I was interested in some kind of art experiment, and Derek was heaven-sent because he gave me this laboratory to kick around in. By the time I'd finished working with him, I was this strange kind of underground film star. Which," she laughs, "I never had any illusions about since my friend Henry Rosenthal said, "Remember Tilda, being called an underground film star is like being called a jumbo shrimp?"
Jarman died in 1994 from an Aids-related illness. Swinton went to 45 funerals that year. Partly in response to losing Jarman and so many friends she created The Maybe – an art project at the Serpentine Gallery in London in which she spent one week, eight hours each day, lying motionless in a glass box, on public view.
She was living in London with John Byrne at the time. They had met in 1985 when he designed a play in which she was appearing, and they became a couple in 1989 after he cast her in his television series Your Cheatin' Heart. She felt right away that he was kin to her, and that feeling has not changed. He's also made her life a lot funnier than it was.
"What else?" she ponders. "He means for me a certain Scottishness. It was really meaningful for me to come home to Scotland with him. I never felt right about England, and yet I still didn't feel like I could be in Scotland by myself because people would assume I was English. So coming together with John and coming to live in Scotland when we had our children was a really happy thing, and I'm still really grateful for it."
There is a good chance that one day, not too far in the future, Swinton may stop making films altogether. "That's really what I would like the most." She'll probably move to the island of Colonsay, which has been her home from home since childhood, and start anew as a writer. In the meantime, though, after her lengthy "American infiltration period", she is about to enter a new era in which she has a greater sense of authorship of the films she makes. These include making I Am Love with the Italian director Luca Guadagnini; We Need To Talk About Kevin is likely to begin shooting in the spring, directed by the Scottish filmmaker Lynne Ramsay.
Before that, though, there is Julia, directed by Erick Zonka, in which Swinton plays an alcoholic who kidnaps the nine-year-old grandson of a millionaire. Her performance is phenomenal, a car crash made flesh, and I watched most of the film from between my fingers.
Swinton wanted to make Julia because she liked Zonka and because she considers the way alcoholism is usually portrayed in films to be quite false. "The largest proportion of really interesting, energetic, driven, fantasy-filled, vivacious people I've ever known have been alcoholics," she says. "Yet we are constantly being given this idea that they are kind of hopeless. I think it's being hopeful that might lead one toward being an alcoholic actually. My sense is that alcoholics tend to be so inspired somewhere that they are disappointed by life and have to dull the pain of that disappointment."
She herself is not an alcoholic. She can't drink much at all without getting sleepy or sick. What about drugs? "No, I'm hopeless with drugs. I've always hung out with stoners but I'm a hopeless stoner myself." The one time she took Ecstasy, in New York during the mid-1980s, she sat quietly in a corner for three or four days. "It was very interesting and insightful but not what I had bargained for." It reminded her that she was not naturally noisy. She had been bullied at boarding school by girls who thought her odd because she was so quiet, and ever since she had been forcing herself to act in an extroverted way. "It sounds weird saying this given that the whole premise of our conversation is that I blab on, but I am actually happier being quiet."
It's very hard to get a handle on Swinton. Is she extroverted or shy? Content or restless? Happy or sad? She's certainly complicated. Having spent several hours in her company, it's only now becoming clear just how much more time would be needed to reach any hard conclusions. Interviewing her is like exploring a vast oil field; no matter how deep you drill, there seems no end to the dark, rich stuff seeping up.
Right near the start of our time together she said, "I never expected to be understood", and as she drops me off at Nairn station, I can't help but feel like one of the people in that train carriage with her all those years ago – unable to fathom what's really going on behind Tilda Swinton's inscrutable, indelible, iconic face.
• Julia is released on December 5