FIGHTING through the crowds spewing out of Sloane Square tube station, I spy Harry Potter's nemesis, Professor Severus Snape, sloping by in the sunshine, chewing on a sandwich.
Nonetheless, it must make a change from forever being asked how come he's so good at being bad - Die Hard, Robin Hood: Prince of Thieves and the BBC's Barchester Chronicles, in which he was the slithery Obadiah Slope, a seductive serpent in a cassock. Or, indeed, whether there's any truth in his co-star Lindsay Duncan's claim that audiences used to leave the theatre after seeing him in Les Liaisons Dangereuses wanting to have sex. "And preferably with Alan Rickman."
"Oh, God, it's years since I played the villain," says Rickman wearily. "I haven't played a baddie for ages."
Clearly, the 'best baddie' persona and the sultry sex symbol image bore him to tears and bear no relation to the man himself, who comes across as seriously intelligent, thoughtful and amusing, with a nice line in sarcasm. The wickedest man in Britain? It's only acting, ladies, so stop sending him all those mildly obscene fan letters. "I am a feminist, so I don't understand how you can have this effect on me..." is typical.
The bad news for all who write to him in a similar vein is that Rickman is a one-woman man. He has had the same girlfriend for more than 40 years - Rima Horton, an economics lecturer at Kingston University. Clever, very chic, she has stood twice as a Labour candidate for parliament and lost, unsurprisingly, in cast-iron Tory seats. She also lost her place on Kensington and Chelsea's council in May's local government elections. "She was part of the national shift, so she's a free woman - a dangerous thought," says Rickman, flashing a smile.
They met when they were students at Chelsea School of Art. He was 19; Horton a year younger. She was his first girlfriend, to whom he has remained steadfastly faithful, although they've never married or had children. He carefully guards the sanctity of his private life and that of his many close friends, among them the actors Ruby Wax, Juliet Stevenson, Geraldine McEwan and Richard Wilson. Interviews with him, therefore, are few and far between.
Today is an exception, though, because he has both a play and a film coming to Edinburgh next month. And he and I have met before, years ago, when he starred in Tango at the End of Winter at the Festival. As he shakes my hand - with a grip so firm it makes my fingers ache - he mentions that meeting, out of sheer good manners, I'm sure.
So here we are, at the stage door of the Royal Court Theatre, where, looking elegantly rumpled in jeans, navy pinstripe jacket and black shirt, Rickman is still chomping on his toasted panini. He offers me half - which I politely refuse, although certain women of my acquaintance would have accepted and preserved the crumbs like a piece of the true cross.
He charms the stage doorkeeper into making me a cup of coffee - he has brought his own - and finds us a large, empty rehearsal room, where we talk about the play, My Name Is Rachel Corrie, and his new film, Snowcake. This is not bad going, given the fact that he later tells me, somewhat mournfully and sounding very Eeyoreish, that every day he looks in the shaving mirror and waves goodbye to yet another major role in theatre or film. "Suddenly, you're 20 years too old for all those roles you planned to do."
He was 60 in February. He has always been guarded about his age, since he was a late-starter - he worked as a graphic artist until he was 25, before going to RADA. In 1991, for example, he told me he thought he was "far too old" for Hamlet. (He went on to play the gloomy prince on the London stage the following year for the legendary Russian director Robert Sturua.) When I asked how old he was then, he refused to tell me, snorting, "It's ridiculous; I don't know why there is this fascination with age. 'Alan Rickman, blah, blah,' in brackets..."
The years may be advancing, but he shouldn't moan. The dark-blond hair may be silvering, but not only does he still get big, meaty roles in movies (he has made three in rapid succession, and in Snowcake he even gets bedded by a vampish young woman), he directs too. His critically acclaimed, pitch-perfect production of My Name Is Rachel Corrie, the story of a young American peace activist who was killed by an Israeli army bulldozer in the Gaza Strip, is tipped to be one of the must-see plays on this year's Fringe. He has refused all interview requests about the play, which is superbly designed by Hildegard Bechtler, the wife of Bill Paterson. It has already had a successful run in London, after the original off-Broadway production was dramatically derailed in New York.
Meanwhile, Snowcake, in which he plays opposite Sigourney Weaver (as an autistic woman) and The Matrix's Carrie-Anne Moss (as the aforementioned vamp), brings Hollywood glamour to the Edinburgh International Film Festival. Weaver - an old friend of the actor since they made the sci-fi spoof Galaxy Quest together - will be jetting in to promote it with him.
All this, plus the release this autumn of a film of Patrick Suskind's bestselling masterpiece Perfume, in which Rickman stars alongside Dustin Hoffman. He has also made a low-budget American indie movie, Nobel Son, a darkly comic tale of a dysfunctional family in which he plays a Nobel prize-winning American physicist. "He's an egomaniac beyond belief. It was terribly enjoyable to play, like going back to panto. All I knew was I needed wonky teeth, so I got my dentist to make me a set. I got on the plane with no character and a set of overlapping teeth."
Currently, though, Rickman is rehearsing the Edinburgh production of My Name Is Rachel Corrie, which he has re-cast with 22-year-old Josephine Taylor, fresh out of drama school. Taylor was chosen in March to understudy the Californian-born actress Megan Dodds, who debuted in the role. (Dodds will play Rachel again when the play transfers to New York in October.) "I've never spoken before about My Name Is Rachel Corrie because it's not about me, and I've always been fiercely protective of Rachel's parents, Cindy and Craig, and of Rachel," says Rickman.
He edited Corrie's writings with Katharine Viner, a journalist on The Guardian, the newspaper that published the 23-year-old's e-mail messages home following her tragic death in March 2003. A middle-class student from Olympia, Washington, Rachel joined the International Solidarity Movement in Gaza. Barely two months later she was run over and killed as she attempted to stop an Israeli army bulldozer destroying a Palestinian home.
On the morning we meet, the headlines are dominated by the crisis in the Middle East, so the issues raised by this passionate, poignant piece of theatre could not be more timely. "This terrible situation simply proves that the play needs to be seen, and to go on being seen," he says quietly, "because it comes from a very human perspective and it's not about taking sides at all."
Does he not find it ironic, then, that the original production, at New York Theater Workshop, was "postponed" by artistic director James Nicola, "because of the edgy situation", citing the fact that the prime minister, Ariel Sharon, had recently slipped into a coma and Hamas had been elected? Surely, ironically, the theatre was taking sides? "I don't think so," replies Rickman, who makes no secret of the fact that he is politically involved, a Labour party supporter.
"The real irony for me was that we had a situation where two independent theatres were in some kind of conflict, which, given the world we are living in, was a great pity. I hope that it's resolved now." Nonetheless, when the play goes back to New York, it will be to another theatre, with new producers.
Rickman was quoted as saying that the cancellation of the production was due to "censorship born out of fear", after Nicola revealed the vehement response of Jewish friends and advisers to the play, some of whom regarded it as "a piece of anti-Israeli agit-prop". "Well, I had to say that about censorship, didn't I?" replies Rickman in measured tones, circumflexing an eyebrow. "We can only guess at the sort of political pressure they were under. I don't feel anything but understanding of their problems. In any case, one of the new producers, Dena Hammerstein, is Jewish herself. Who knows? More rocks may still be thrown in our path, because the subject-matter is a hot potato."
Nicola's decision was condemned by Harold Pinter, Tom Stoppard and Vanessa Redgrave, a longtime supporter of Palestinian rights. Now Rickman only wants the play to be seen by as many people as possible. "There are times when a piece of work attaches itself to you in a very deep way. For this important play to be turned into a personality thing would be inappropriate; that's why it's not about me."
Rickman read Rachel's e-mails in the newspaper. "Two things stick in my mind: one was that the writing didn't feel as if it wanted to be trapped on a page for ever, it wanted to be spoken. The second is, I might not have read that paper, just as I haven't got round to reading one today - I might not have known," he says, trying to imagine the unimaginable.
Immediately, he left his home in west London and went to the Royal Court to suggest to Ian Rickson, the artistic director, that they should do something with it. "Then Rachel's parents arrived in London. They were a bit dazed, not just by what had happened to their daughter, but because this theatre was saying, 'We want to do a play based on her writings.' But they are remarkable people. There was never any bitterness or anger, only reasonableness and a desire for justice - because there has never been an investigation into Rachel's death."
The Corries gave Rickman "everything" - Rachel's school notebooks, jottings, diaries, poems. "We got 182 pages, from the time she was 12 up to the Gaza e-mails. I went to the Corries' home, in Washington, and spent time with them. 'Don't put her on a pedestal,' they said to me. But I was always concerned that this would not be a 90-minute polemic. You come, you make up your own mind," he says. "Of course, when Cindy and Craig saw the play, they were like human waterfalls."
When I saw the production, I veered between wanting to shake Rachel for her naivety and wanting to embrace this "scattered and deviant and loud" young woman for her intelligence, spirit, honesty and courage.
"I'm so glad you felt that, because that's exactly how I hope audiences will feel," responds Rickman. "This isn't a play about Palestine or Israel, it's about being a citizen of the world."
The play ends with a video of a ten-year-old Rachel galvanising her schoolmates with a speech about world hunger. "People say to Craig and Cindy, 'Who wrote that for her?' Unbelievable! But that's not as bad as the person who said at one after-show discussion, 'It's just a pity you couldn't get a better actress for the video at the end.'
"The crucial thing for me about the play is that it corrects the slanders on the internet about Rachel and the way she has been demonised - such as, 'Did you know she was a member of Hamas?' She was just this normal, all-American girl who cared. Do I know her? I go to their home - what Rachel called 'a doll's house, floral world' - and I realise I don't know the half of it. There are all those family photographs on the piano - another life.
"I know Rachel only as I know any character, the way I know Alex Hughes, say, the man I play in Snowcake, who is probably more like me than anyone I've ever played. He's very close to me, because I enjoy playing somebody who is just doing his best - that's me."
If Rickman is Alex, he's also an honourable man with an enormous hinterland of grief and guilt. A kind man - as Carrie-Anne Moss tells him in the low-budget Canadian film, which opened this year's Berlin film festival - who has "a face with interesting baggage". Or, as Alex responds drily, "In my case, haulage."
Rickman asks me not to give away how he ends up caring for the autistic mother - Weaver's character - of a young hitchhiker. But you'll need the Kleenex as the frozen wastes of Alex's heart thaw and Weaver enjoys the orgiastic pleasures of snow. "I love that movie; I hope people get it," he says. "It's funny, full of light and hope. Great friendships were made on it. By the time the money needed to make it was eventually raised, it had stopped snowing in Wawa, in northern Ontario, where it's set, but the locals saved snow for us in their sheds and garages."
With Rickman bespectacled and in an anorak, it's all a far cry from the lace cuffs of the vulpine Valmont in Les Liaisons Dangereuses, or indeed the truly madly creepy Professor Severus Snape.
HE may have aristocratic looks, but Alan Rickman was raised on a council estate in Acton, London. Of Irish-Welsh parentage, he is the second of four children. His father, Bernard, a painter and decorator, died of cancer when his son was eight. That silkily sexy, languid tone and delivery are the result of a speech impediment he was born with - the award-winning actor cannot move his jaw properly, which gives him a voice unlike anyone else's.
At 12, he won a scholarship to Latymer Upper, a private school in Hammersmith (the alma mater of Hugh Grant and Mel Smith), where his interest in acting was piqued. He and Rima did am-dram shows together until Rickman finally applied to RADA. One of his first major roles was at the Citizens Theatre, in Glasgow, where he was in Giles Havergal's renowned 1980 production of Brecht's Fears and Miseries of the Third Reich. "Layers of authoritarian corruption are laid bare with merciless economy and real glee," wrote one critic of Rickman's performance. "I can't tell you what it meant to know that the Citizens would give you an audition if you asked - and, if they thought you were pretty enough, a job. I miss it. They changed all our lives," Rickman says, adding that he is planning a return to the stage soon. "It's still under discussion," he says, adding that it will be the first piece of theatre he has done since Private Lives, in the West End in 2001.
In the past year, Rickman has worked and travelled incessantly. Perfume, directed by Tom Tykwer, who made Run Lola Run, was filmed in Barcelona, on a budget of 35 million. "The malodorous world of 18th-century Paris is brilliantly conjured up in the film, which is very beautiful," he says. "I love perfumes. Every morning when my girlfriend and I come down to the courtyard in our block of flats we're assailed by the most delicious scent - jasmine round a doorway. It almost makes me swoon."
There, I think, you have the contradiction that is Rickman: an actor who can do bad-smell-under-the-nose disdain to the manner born and a guy who makes time to sniff the posies. But, ladies, I beg of you, do not bombard him with bouquets of jasmine. Just carry on lusting in the privacy of a darkened auditorium.
• My Name Is Rachel Corrie, Pleasance Grand, August 5-28; previews August 3 and 4 (www.edfringe.com); Snowcake, Dominion, August 15; Cameo, August 17 (www.edfilmfest.org.uk)