Sadly, being rich didn’t help Scarry sleep last night. Today, she has a nerve-racking art crit lined up at college. Also, The Sunday Times is on her trail. It’s been made clear from the outset by Scarry’s model agency, Storm, that Scarry is not, repeat, not the new Paris Hilton. She will let Style hang out, but only if nobody uses the dreaded description, the one that every young female jet-setter fears and despises above all others: “It girl”.

On first impressions, it’s true that Scarry doesn’t conform to the universal It girl template we have all come to know and love. Where, after all, is the Dolce & Gabbana? Where is the St Tropez orangu-tan? The empty eyes and juicy collagen pout? This girl is wearing a simple black Gaspard Yurkievich top, a Hussein Chalayan skirt, a Zac Posen shawl and Marc Jacobs heels. She is polite and understated, with a gentle aristo charm. And if she is feeling shifty about me, she isn’ t showing it.

As Style is to spend the day with an heiress, we have laid on a silver Rolls-Royce Phantom with driver. We thought Scarry might like it. “Oh no, we’re in a Roller, going down Portobello Road. How embarrassing!” she gasps, as we head away from the Christian Louboutin sample sale and towards Notting Hill. “When we lived in France, my father used to collect vintage Silver Clouds. My sister and I would duck so we didn’t get spotted by any of our friends.”

We park at the arty end of Portobello, outside the office of the hip lit magazine Zembla. Scarry is right at home in the soft boho poshness of this corner of town. The 22-year-old has a meeting scheduled with Zembla’s editor, Dan Crowe. They’re collaborating on a project involving her late grandfather. Nobody’s yet sure what form this collaboration will take, but everyone concentrates hard, which must be a good sign.

The next item on today’s schedule is Willma, a fashion boutique that’s having a closing- down sale. Scarry scans the bargains with the expert eye of a born fashion editor. She likes Alexander McQueen, Rick Owens, Issa and Vivienne Westwood, not the standard Eurotrash diet of Dior and Cavalli. “I don’t go shopping as much as I used to,” she says. “When I was younger, I went shopping every day after school. My bedroom was opposite the seventh floor of Barneys. God knows who paid.”

Back in the purring Roller and having bonded over clothes, Scarry begins to shed the caginess she has been disguising with impeccable manners. She describes the six years of palatial, familial reverie in Venice, before her parents separated and she moved, with her mother and sister, to New York. This was wild. The family rented a suite at the Ritz-Carlton and the girls enrolled at the exclusive Convent of the Sacred Heart. Scarry became best friends with Nicky Hilton and, by 16, the two were gossip-column perennials, known for their decadent parties. Are they still in touch? She pauses. “I love Nicky and we used to be close,” she says, “but we’re quite different now.”

Scarry is very discreet, but the jet set’s horror at the rise of the gaudy Paris is well known. The Hiltons may not be invited to fabulous private gatherings in German schlösser and Italian palazzi this summer. In high society, such flagrant self-promotion is, like, so totally last year. Understatement is in.

We’re now at the college where Scarry studies a very 21st-century combination of fashion illustration and world environmental policy. Who knows what her friends think of her bringing a journalist into class with her — perhaps it happens all the time? Scarry’s work gets a pasting by the tutor, but she seems to take it in her stride.

As we leave, she says: “My father is an artist, not a businessman, and I think it’s the most amazing thing, if you’re shy, to be able to express yourself through art.” I don’t tell her what I’m rather ungenerously thinking: that pursuing your art without worrying about selling it is, these days, mostly the preserve of the privileged.

At 4pm, Scarry has her first ever model casting. She was “discovered” last year by the fashion stylist Isabella Blow — friend and mentor to so many lovely young society types — who took pictures of her for Tatler wearing white mink (Blow told Scarry that mink was “very her”).

Scarry is underwhelmed by fame (“I wouldn’t mind ... if it were for the right reasons”), but she likes being photographed. At 18, she started dating Nellee Hooper — the big-noise music producer from Bristol who has worked with U2, Madonna, Björk and Gwen Stefani — and for two years she was photographed at all the A-list parties. “We both love to travel, so we went all over the place and it was loads of fun,” she says with a look that suggests she wishes she were somewhere else.

Yes, yes, but what was P Diddy like? “We were with him and others in Sardinia, and I wondered, ‘So who is this Puffy guy?’ But then we spent two weeks together, just me, Nellee and Puffy, relaxing, sunbathing and watching videos, and he turned out to be the sweetest man ever.

“I also really like Bono,” she says. “To hang out with, he’s up there with the coolest guys I’ve ever met.”

We’re on our way to Tate Britain, but divert to Topshop. This weekend, Scarry is off to a party for 700 thrown by friends in Rome. The theme is “fluorescent” and she needs some Day-Glo hair extensions to go with an old Chloé bikini and her mother’s orange vintage Courrèges coat she’s planning to wear.

An hour later we’re at the Tate, where Scarry’s heroine, the artist Vanessa Beecroft — a feisty, imperious lady who made her name creating performance art involving groups of women in various degrees of nudity — is talking to a rapt audience.

Afterwards, while I’m getting a glass of white wine, Scarry vanishes. I look for her in the queue for signed books, but she isn’t there. She reappears five minutes later, breathless and pink. “I introduced myself to Vanessa and told her I loved her work. And I asked her if I could be one of her models,” she says.

Could Scarry, a girl who appears to have everything, become an artist’s muse, too? Of course. Why ever not?

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