The last time I saw Lily Cole was at a dinner party. She was sitting at the other end of the table from me, chatting merrily with Amy Winehouse’s bloke, Blake Fielder-Civil. Tongues were wagging long before Winehouse turned up after spending the previous three hours circling the block in a car with her hairdresser. By the time Wino arrived, her entourage had gathered in a corner to discuss matters furiously. How dare Lily talk to Blake? An hour later and Amy and Blake were barricaded together in the loo, with the Olsen twins standing outside promising them free late-night shopping at Harvey Nichols if they’d only open up. Did Lily, who had long disappeared, have a clue what she’d started?

Cole, 20, doesn’t strike me as the type to waste time on someone else’s sexual psychodrama. Today, sipping tea in a South Ken cafe, hair tied back, a little make-up on her face, she has other things to worry about. Such as a course in social and political sciences at King’s, Cambridge, which she is finally starting in September. And the shirtdress she is wearing. “If I leave it undone, it shows too much. If I do it up, it’s prudish.”

Obviously, she’s a star — seven international Vogue covers, some 17 ad campaigns and a fledgling acting career, including a lead role in Terry Gilliam’s next flick — but she is not a tabloid star. Nor is she, in truth, a fashion icon: I don’t think she cares about clothes enough. But magazine editors die for her. The otherness of her face, the opposite of everything cheap and overfamiliar, is fashion catnip. She isn’t of this world; she’s a creature from somewhere out there who happens to have chosen glossy paper for her earth landing. Her sex appeal — at the end of last year, Juergen Teller shot some arresting naked photos of her for an upmarket men’s magazine — is certainly not come-hither. If anything, it’s on the pervy side.

Since scandal has been distinctly lacking in her career, the current topic of public discussion is the Storm model’s decision to start at Cambridge University after deferring for two years. The announcement made the evening news. Model risks career for learning!

“I’m not sure why everyone is so interested in it. It’s quite a small gesture really. And I always knew I was going. I know what I’m like and if I don’t go, I’ll always wonder. It’s a little scary but when I freak out, I think, ‘Get over yourself, Lily.’ ”

She is the latest in a line of photogenic brainiacs making headlines by choosing the path of the bluestocking. Natalie Portman did it; so did Jodie Foster. Yet her decision seems of-the-moment. Nerd is in. The charts are full of cerebral bands such as Vampire Weekend, Foals, Battles and We Are Scientists.

“It’s bizarre that people find it so fascinating. I take opportunities as they come. Fashion has been a great one, but it hasn’t stopped me doing other things. I love creativity and I’m interested in the humanities. Human life, art, any of those things wonder and perplex me.”

Anyway, Cambridge’s three eight-week terms a year will mean the fashion massive won’t ever have to wait long for her.

She is, predictably, grown-up beyond her years. She’s been everywhere. “I went to New Orleans the other day. I loved it so much I could move there! I love Kenya — there’s a freedom of living with no inhibition. I was just in the Rockies, which were great. And I love the Himalayas. And India. And I love Japan. Such a nutty place — but the people are so gentle.”

How will life not bore her from here on in? She delivers lines such as: “It’s a sad fact, but then there are a lot of sad facts in the world.” And: “As the Dalai Lama says, ‘Money will bring you friends, but they’re not friends of you, they’re friends of your money.’ It’s the same with being fashionable. People are so attracted to that, and it’s important to understand the difference.” Unlike many of her peers, when the time comes to retire, she’ll go deep (books, art) not wide (album of Kylie Minogue covers).

She was an outspoken campaiger for environmental and humanitarian issues when it was deeply unsexy to be one, particularly in the world of modelling. While other mega-models pay lip service to ethics — a fashion shoot wearing eco-friendly labels, perhaps — Cole adopted, among others, WaterAid and the Environmental Justice Foundation as her pet causes. She signed up to M&S because of its Plan A green initiative. She cut her relationship with De Beers because of the diamond company’s treatment of native Bushmen.

“It isn’t that I want to be vocal, but if I have to be vocal about something, I’d rather it was that than me talking about myself.”

She’s still a model, though. One who’s earned an estimated £6m from her face and body. How does that square up?

“I feel so lucky. I always wanted to do creative things when I was younger and I wondered how I’d afford it. I’m lucky to have the freedom to do things I want.”

She says she’s even started to be less serious. “I’m enjoying being around my friends. I can get too heady when I’m on my own. Now I just want to frolic about a lot.”

Last night she saw her favourite band, Sunset Rubdown, play a gig. “Watching them made me want to dedicate my life to music. They were geeky and totally into it. That to me is cool.”

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