Alexa Chung talks and thinks very fast. She’s full of stories and takes the mickey out of herself with a nice combination of faux puzzlement and sarcasm. When the paparazzi chase her around, she sometimes stymies them by standing very, very still, like those human statues in Covent Garden, so they get the same picture over and over again. She says she still wonders what it is they are taking pictures of: “Like, Alexa Chung, television presenter and It girl? I mean, there’s not much to being an It girl. It’s really quite a depressing title to hold.” If it were a job, what would it entail? “Well, for me, it would be a charity-shop coat, a Mulberry bag, drinking champagne at a bad party and having a boyfriend in a band.”

Chung’s star has been in the ascendant since April 2006, when she started presenting some of Channel 4’s youth programming. She now has plenty of television offers and a magazine column, and is a must-have at any self-respecting fashionable party. People adore her style, and, as with Kate Moss and Sienna Miller, I’m sure a lot of young girls ask themselves, what would Alexa wear? For the past six months, she has been seeing Alex Turner of Arctic Monkeys – a fairly big step up from your average lanky bloke in skinny jeans. In a short space of time, she has captured a pretty chunk of the hip young zeitgeist for herself.

“You’re not going to talk about Turner, are you?” she says, her voice flattening. “It’s sad to think girls are famous for their boyfriends. I don’t want to be one of those. Going out with him is just like going out with any boyfriend, except he goes away a lot and people pester me more for guest list.”

She was brought up in Hampshire by her English mother, Gill, and first-generation immigrant Chinese father, Phil. It was a nice middle-class upbringing. “Me and my sister went to the local comp, Perins, and my brothers went to private school – but not a good one. I had a horse: maybe that’s where my money went. I’d like to have one now, and a boat. I love horses ... Look.” She fi ddles with what looks like a heavy silver horse hung round her neck on a piece of cord. I go to touch it; it is made of the lightest plastic, and one of the legs has snapped off. “My boyfriend got it for me.”

I first met Chung three years ago when she was a model going out with my friend David Titlow, a photographer, who was much older than her. She went out with him for a long time, and talks of it with a lot of love and as “an education” – she describes herself as a 60-year-old in a 24-year-old’s body. She says that Turner shares those old-person interests – “He’d never want a Wii or anything.”

At the time, we hung out a bit. She was confident and amusing, if plagued by an all too familiar tendency to describe herself as fat. “Modelling gave me a distorted body image. As soon as I stopped, I realised how ridiculous it all was. I went on about it because I was really fed up with modelling – it’s like I was saying negative things to reinforce in my mind that I had to get out. I never say or think those things now. I’ve used up all that neurosis – there’s none left. It’s just really boring. I’d rather have a bigger brain than smaller bones.”

Still, it ate into her soul a bit, the job of modelling, there’s no doubt about that. “It was the saddest thing. I’ve got pictures of me in Thailand on my 21st. I remember I didn’t eat any birthday cake. It was all, ‘Oh God, no, I can’t have rice.’ I see those pictures and I’m, like, God, you look so ana. I saw a girl the other night who I used to work with. She’s still modelling and we talked for ages. At the end of the night, Turner said, ‘Why did you spend the whole night trying to coerce that girl into doing something different?’ Modelling erodes self-confidence. Maybe it’s not true for everyone – I hope it isn’t.” At the time, she was thinking about acting or photography – she still sees them as possibilities. She got two As and a B at A-level, and is “still pissed off about the B in history”. She started acting, then was called up to audition for the T4 show Popworld. She made the transition with consummate ease: “It’s just an extension of modelling, really – cameras are cameras.”

She quickly found her feet. “At fi rst, when people asked my opinion about a script or something, I was, like, ‘I’m sorry?’ But before long, I was saying, ‘Yup, that’s wrong, let’s change it.’”

I suspect that what makes Chung likeable to the female population is that she is not trading on her looks or her sex appeal. She is a tomboy who genuinely loves music, does not see clothes as status symbols, and is not one of those “I’ll look better than every other woman in the room” competitive types. “I either want to look like an excellently dressed boy or a kitten from the 1960s,” she says. I mention Miller in Factory Girl. “No, more like Françoise Hardy. At the moment, I want to look like Princess Diana. The other night, someone said I looked like a mum at the school gates, and I was, like, ‘Thank you.’”

She says she can be confrontational and argumentative with men in authority, and suspicious of being sidelined: “Sometimes I think I go on the attack too much.” She will likely become an interesting handful for producers or directors with bad ideas, because she reads, is informed and is not afraid to have strong opinions. When we talk about things, she can formulate a solid argument – we have a random and amusing exchange about the evolution of the whale. I doubt she’ll be a TV presenter for ever: she envisages going to university in her late twenties, to study English literature, then becoming a photographer. Even though she is very much the girl of the moment, she has absolutely no sense of herself as special. “You cannot be a TV presenter and be cool. No, you are merely a conduit, asking people questions. You are always the douche bag, extracting information about other people’s awesome lives.”

And so, with another piece of cute self-deprecation, she picks herself up to do some Christmas shopping. We go to Marc Jacobs, where she finds a £20 T-shirt with a clown on it. She says “It makes me feel happy”, and buys it. We walk off to Oxford Street, me uncomfortable in heels, her striding out in flats. She wonders what to buy Turner for Christmas. There’s talk of Graham Greene’s Brighton Rock and a great box she has found that she’s going to fill with cool stuff. She says: “Life’s all right. It’s really nice right now.” To the point where she wakes up every morning full of beans? “No, I wake up every morning going, God, how early is it?”

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