If Uma Thurman ever decides to give up Hollywood — and she has done so before — she could run an excellent course for aspiring starlets. At 38, she has developed a rather unnerving natural authority. And, my word, she has lived the life: teen stardom, tabloid marriages, sinister stalkers, a career that has oscillated between modern classics (Pulp Fiction) and outright stinkers (Even Cowgirls Get the Blues).

Yet here’s Uma, battle-weary and still going, all 6ft of her taking up plenty of room in a suite at Claridge’s hotel, in London. She looks marvellous in the flesh; perhaps even more glowing since the announcement of her engagement to Arpad Busson, 45, the famed multimillionaire hedge-funder and philanthropist. She met him on the glitter circuit a year ago, introduced at a party Donatella Versace threw for Tony Blair in Milan.

“Personally, things are wonderful,” she says breathily. A naughty smile creeps across her face.

“I’m going to have to retract my statement of never.” Thurman notoriously vowed, after two failed marriages (to Gary Oldman and Ethan Hawke), that she wouldn’t marry again. She now has an engagement ring so big, she can barely get through the sleeve of her coat. “I’ll have to eat my words — what a surprise,” she trills. Oh, Uma, that’ll be three marriages before 40. “Let’s not mention that,” she says, puckering her lips in mock primness. Nothing, not even exes, is going to overshadow her excitement.

Thurman has a Swedish mother, and there is more than a hint of Valkyrie about her — the height, for starters, plus that equestrian nose, with its quivering nostrils, hands the size of dinner plates and throaty tones reminiscent of Garbo. Indeed, she is here today not as an actress, but as a model. For some years now, she has been the face (or should that be wrist?) of TAG Heuer watches. She likes the watches, but thinks this strange. “I can’t remember the last time I gave an interview without having a film out,” she says grandly, lowering herself into an armchair.

I tell her, somewhat redundantly, that she’ll make a beautiful bride. She rolls her eyes. Thurman cares not for the flattery of mere mortals. “Oh, come on. I look my age, and I don’t mind. Everyone looks their age — some just look a little bit more fantasy.” There’s no suggestion of a surgeon’s knife on Thurman’s CV. “Being in my late thirties is fine with me. Maybe when 40 hits, the penny will drop and you just hate life. But so far, so good.”

Actually, it hasn’t always been good. As a child, didn’t she feel awkward about her looks? “I didn’t feel awkward, I was awkward,” she cuts back. “It’s such a cliché, but it’s a truism that tall, gangly women who end up all right later in life are always ugly children. I was funny-looking. I mean, look at my hands,” she cries suddenly, holding them up. “Imagine having these hands at 12! By the time I was 13, I was easily 5ft 10in. Can you imagine? That’s a mess.”

Her ugly-duckling syndrome can’t have been helped by coming from a line of top-notch beauties. Her Swedish grandmother was so exquisite that a statue she modelled for overlooks Smygehuk harbour to this day. At 14, her mother, Nena, was scouted by Norman Parkinson in her school playground in Stockholm. “He gave her his card and said, if she ever wanted to leave Sweden, to give him a ring.” Nena did, and by 16 was wowing Paris and New York, appearing on the cover of French Vogue — a bona fide supermodel.

Salvador Dali introduced Nena to her first husband, Timothy Leary, the controversial 1960s psychologist who advocated LSD use. The marriage didn’t work (go figure), and Nena married Thurman’s father in 1967. Robert Thurman has the honour of being America’s first Tibetan Buddhist monk, and is now professor of Indo-Tibetan studies at Columbia University. Thurman and her brothers all have the silly names to prove it. Her full name is actually Uma Karuna, poor love. But there were upsides. On the family’s long sabbaticals to India as children, she remembers the Dalai Lama popping round for tea. “It’s no credit to me, though,” she says of the experience. “It’s my father’s world, so I don’t feel honest borrowing any of that spiritual or intellectual glamour. Let’s just say it was interesting.”

In her teens, Thurman was yanked around several schools, but — in the time-honoured tradition of social outcasts everywhere — found solace in the drama club. She segued from school plays to silver screen with terrifying alacrity, appearing topless, at 17, as the goddess Venus in The Adventures of Baron Munchausen. At 18 — again topless — she held her own against John Malkovich and Glenn Close in Dangerous Liaisons.

In retrospect, there was something a tad pervy about Thurman’s early roles. She was, in her own words, “a child actor”, and “certainly wasn’t very comfortable with it”. She took to wearing baggy clothes and eventually fled to live in London for a year, where she met and married the British actor Oldman. As with her mother’s first marriage, it lasted less than two years.

Her most famous role, as Mia Wallace in Quentin Tarantino’s Pulp Fiction, turned her from starlet to star. “The mid-1990s were huge for me, but then I threw it all away and had children,” she announces dramatically. Was Hollywood really so matter-of-fact? “Oh, yes. People basically said, ‘Sayonara.’ Obviously, I was in my prime, at the top, and that shut it all down. But I wanted to shut it down. I wanted to have a family more than I wanted another 10 jobs.”

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