Interview: Sophie Dahl, model and TV presenter

Her size-14 curves made her more real-world than planet couture, and she became an overnight sensation as a long-overdue poster girl for women who simply weren't born to be skinny.

In her love life, too, Sophie has shown a single-minded determination to do things her way. There was much tut-tutting about her relationship with ageing rocker Mick Jagger, 34 years her senior. Then, three years ago, she met jazz singer Jamie Cullum at a charity do – Dahl sang I Think It's Going To Rain Today by Nina Simone and Jamie accompanied her on the piano – and it was height rather than age difference (Sophie is 6ft; Jamie 5ft 4in) which made them, yet again, the subject of tabloid mockery. A less secure woman might have buckled under such unrelenting scrutiny. Ms Dahl got married.

Now, Sophie could find herself breaking a mould (or two) for real as she makes her debut as a TV cook in The Delicious Miss Dahl on BBC2 this week. The series, the result of collaboration between Sophie (who used her book, Miss Dahl's Voluptuous Delights, as inspiration) and Jamie Oliver's production company Fresh One, focuses on a different emotional theme every week, ranging from romantic to melancholy.

Chatting over a cup of green tea in the press office at BBC HQ in Shepherd's Bush, she declares herself really quite chuffed with the programme.

"It has been a very happy marriage between me and the production company," she smiles. "I would never have got involved in something that just meant turning up at eight and leaving at five. I really wanted to be true to myself, my books and my cooking. When I write about things, it's a lot to do with sense memory. How things smell and taste can bring incredible memories flooding back and transport you in an instant to another time and place. Food can be a form of magic and I really think we've captured it in the programme."

What the programme certainly does capture is Sophie's unapologetic love of times past. In an exquisite house decorated with hand-tied bunches of peonies and gently billowing antique lace curtains, she whips up divine dishes – rich chocolate pots with brandy-soaked cherries are a highlight – before retiring to a perfect English garden to read excerpts from her favourite books while basking in the late afternoon sun.

Like the tooth-hurting peanut butter fudge she conjures up in this week's programme (pure indulgence food, in keeping with the programme's Selfish theme), the show could be in real danger of being sickly sweet. Thankfully, our host's genuine – and highly infectious – love of nostalgia brings a necessary balance.

"I know it's like a version of life that's better than it really is… but wouldn't it be lovely to be wafting through a house like that?" asks Sophie. "I've always found the immediacy of our culture a little bit hard-going. I know part of nostalgia is romanticising the past, but I love doing things in a slower way, and the glamour of bygone eras. I've got to confess … I do feel slightly like I've been born in the wrong time."

She may have a point. In the flesh, she is utterly mesmerising, reminiscent of a 1930s screen siren. After shedding those famous curves – "It happens to all the Dahl women; I was an unfortunately round teenager and then I willowed out in my twenties", she explains – Sophie (at an estimate) is now a healthy-looking size 10. She attributes this to three sensible meals a day ("no picking!") and yoga and Pilates (though she admits to not having come into contact with a yoga mat for the past six months).

But it's the face that really gets you. Those huge, pool-like eyes, perfect rosebud lips and creamy skin – she's like the original Pear's soap girl, all grown up. Refreshingly, however, Sophie – who is 32 – doesn't seem overly aware of the effect her looks have on others.

"It actually makes me feel sick, watching myself on TV; I can't bear it!" she laughs. "I watched the first edit – to help contribute ideas for the soundtrack because I had lots of lovely songs in my head for the series – and you become acutely aware of things that nobody would tell you about in real life. I say 'sort of' far too many times and there's a kind of grimace I do when I'm trying to make a point which makes me look just like my dad. Not good!"

Ah, Sophie's family. One suspects that her yearning for a perfect past might be a reaction to the reality of her own early years. Her parents – Tessa, the daughter of legendary British author Roald Dahl, and actor father Julian Holloway – split when Sophie was still a child.

A bohemian childhood followed; she attended ten different boarding schools in England and lived in 17 countries, including Britain, America and India. Sophie famously inspired her grandfather to name a character after her in one of his books, The BFG. Coming from such an extraordinary family, did she feel real pressure to earn her place in the Dahl Dynasty?

"You've got to remember that to me, my granddad was quite pedestrian," she says. "Yes, I would occasionally sit on his knees – which were terribly creaky, by the way! – while he told me a story. But he was just granddad to us.

"To be honest, I didn't feel any pressure – in some ways, it had the opposite effect. It made it seem possible to do anything. Had I grown up in a family where my dad was an accountant and my mum was a nurse, I might have felt more pressure to do something more nine-to-five and not feel there was anything valid about going into the arts."

In between modelling and acting ("I was a horrible actress, and you won't have seen any of the films I was in") Sophie discovered she had indeed inherited her grandfather's remarkable way with words. Her first novella, The Man with the Dancing Eyes, was published in 2003 to critical acclaim. Her novel, Playing with the Grown-ups, made the shelves in 2007 and another cookery book and work of fiction are in the pipeline.

It was Sophie's beloved Scottish nanny, Maureen, and Gee Gee, her grandmother, who provided much-needed stability in her peripatetic childhood and continue to inspire her today.

"Nanny Maureen looked after me from the age of one. She finally left last year, when my little brother reached 15. I used to spend every New Year's Eve with Maureen and her family in Edinburgh and go first footing with her. I still speak to her often. She features a lot in my cookery book – she is the queen of lentil soup and makes the best rice pudding."

Judging by the smile that lights Sophie's face when she starts to talk about Gee Gee (whose real name was Violet), it's obvious that some of her happiest childhood memories involve her paternal grandmother.

"She taught me to cook. She was a real cook, growing vegetables in her garden in Angmering-on-Sea in East Sussex. I love that whole rhythm of living – you grow stuff in your garden, then visit the fishermen to get your fish they've caught that morning. It was all before it had names like 'seasonal' – it was just common sense. Our grandparents were doing it years ago and not even thinking about it."

However, Gee Gee was no domestic drudge. As a jobbing chorus girl in the 1920s and 1930s, she met and fell in love with well-known actor Stanley Holloway, who is perhaps best known for playing the cheeky stationmaster in Brief Encounter. In fact, like Sophie and Mick Jagger, her grandparents' relationship caused quite a scandal.

Sophie leans forward, conspiratorially. "Stanley was 26 years older than her and had been married before so it was very scandalous at the time," she explains. "But they absolutely adored each other and they were together until he died."

If there was ever a golden moment to ask about her own wedding, this would be it. But Sophie has made it clear that the subject is a no-go area. Details of the couple's big day are sketchy, although it was confirmed that the pair tied the knot in a winter-wonderland themed venue at Lime Wood Hotel in the New Forest.

But I do ask about a delicious quote I discovered while researching for the interview, when Sophie said: "My idea of happiness is being incredibly rich, living in Italy, barefoot in the kitchen and pregnant."

"That quote is always coming back to haunt me," she groans. "I would never have said something like that about being rich. If I'm surrounded by people I love and domesticity, that's pretty lovely."

Home for Mr and Mrs Cullum is either their place in West London or a recently renovated house in the country. In previous interviews, Sophie has painted a real picture of domestic bliss, with the pair pottering around their home. So does Jamie compose his next hit song while Sophie cooks up a storm in the kitchen?

"How grim," she laughs. "No, it's not like that at all. Jamie is actually a great cook. He was great when I was filming – after cooking and tasting all day, all I would want to do was come home, have a long soak in the bath and a glass of red wine. So Jamie would cook something. And the one thing he is definitely better at than me is poached eggs. He can just drop them straight into the water and end up with these perfect little nests."

Sophie says it's mostly male TV chefs and writers that get her taste buds tingling. Simon Hopkinson, author of Roast Chicken and Other Stories comes in for particular praise, as does Nigel Slater and his series, A Taste of My Life, in which celebrities reminisced about their own favourite food memories.

But is she prepared for the inevitable comparisons that will be made between herself and Nigella Lawson?

"Can I just say that How to Eat is one of my all-time favourite cookbooks. Nigella is a legend," she says. "I get the whole media thing of wanting to create headlines and fostering some kind of fake competition.

"I think we have a particular compulsion in this country to pitch women against each other. It doesn't happen so much with men – with the male chefs, there's a bit of jokey camaraderie. But with Nigella and myself, we are both nice, middle-class English girls, both not properly trained chefs … so of course it's got to be knives at dawn. When it's really not!"

Knives or no, Sophie could certainly do with some body armour to deflect the inevitable barrage of well-meant comments from people on discovering her newly-wed status.

"That's the awful thing about when you get married," she laughs. "I was in a taxi the other day and the driver asked me how old I was. When I said 32, he said 'Well, you'd better hurry up, time is ticking on'. I was like, 'Hmm, do we actually know each other?' But yes, children are on the agenda, absolutely. I just don't know when. I'm getting my fix from friends' babies at the moment, so we shall see."

Plenty of time to squeeze in a few more breaking-the-mould moments then.

The Delicious Miss Dahl, Tuesday, 8:30pm, BBC2.

• This article was first published in The Scotsman Magazine on Saturday, March 20, 2010