It’s one of those names, isn’t it? You hear “Versace” and your mind fills in the blanks. Gold-plated taps, acres of marble floor heaped with busy antique rugs, rococo end tables, crystal chandeliers and medusa heads winking at you on everything from the scatter cushions to the loo seat.

This was what I expected as I fought my way through a late-morning crowd of well-heeled tourists, lunching ladies and assorted Eurotrash in Knightsbridge, west London. For a start, the whole neighbourhood is defiantly bling and, at 27, Francesca Versace, Gianni’s niece and a fledgling designer herself, has lived in this fancy postcode for seven years. Weaving down a cobbled mews opposite Harrods, I find the small modern development of flats she calls home, take the lift and stand outside a paper-white door.

Then the door opens and . . . huh? It’s not bling at all. Francesca, immaculately turned out, is standing in her kitchen in a purple Vivienne Westwood sweater dress. It’s the most riotous splash of colour in the place.

The vibe in her two-bedroom flat, which she has owned for five years, is shockingly similar in spirit (if not price tag) to the post-student dwellings of many a former graduate. It has that unmoved-into look, a transience that befits the homes of yoof who prefer to work, party and travel, rather than nest. The shelves are stacked with her old course books and the coffee table piled with knick-knacks. Her desk is a clutter of photographs and sketches. She even has one of those teenage-style collages of torn photographs of her friends on the wall (but obviously, as it’s her, these include pictures from Tatler and snaps of Linda Evangelista).

Still, it’s all rather normal. There’s no sign of a liveried butler or an adonis in a loincloth wafting a palm leaf. If she didn’t have that subtle look of super wealth, she’d be indistinguishable from a million other young professionals who come to the city.

Of course, Francesca already had the name, and her upbringing was anything but normal. The daughter of Gianni’s elder brother, Santo, who has managed the business side of the Versace empire since 1976, she grew up in Milan in the thick of air-kissing fabulousness. As a child, she hung out with Kate Moss, Naomi Campbell and Christy Turlington backstage at the Versace shows at the height of the supermodels’ fame. “I loved Claudia Schiffer. I was obsessed,” she laughs. “I was only 11, but I always made her have her photo taken with me.”

She attended a local German school — her father insisted it was the best foundation to learn other languages — but by her midteens, she knew she wanted to go into the family business. She is very close to her aunt Donatella, who runs the creative side of Versace and took her to visit the fashion department at Central Saint Martins when she was 17.

Francesca fell in love with the school and the city, but was hurt when her first application was rejected. The gossip columns crowed, but she picked herself up and applied for another foundation course to improve her chances. “I went to the London College of Fashion and did business and pattern cutting, which I hated, but reapplied for Saint Martins and finally got in. The first year, I was crying all the time. All the teachers gave me such a hard time.” To prove a point? “Exactly,” she says. “But I did three years and I loved it. I had so much fun by the end.”

Since finishing her degree, she has shown a collection under her own name — Francesca V — in Paris, but has recently made a move into interiors. She will oversee room decoration for a new resort her father is building near Venice and is in the throes of doing up her first “grown-up home” in a street round the corner in Knightsbridge.

She can tire of the chichi, west London scene, though. She’s also, rather uncoolly, into inline skating. “I learnt how to do it when I was in Miami.”

When were you in Miami, I ask carelessly, before realising instantly this was where Gianni vacationed and was shot dead outside his home in 1997. She isn’t offended, though, and pulls a Sotheby’s catalogue off the coffee table to show me some of the delights it auctioned from one of his other spectacular homes on Lake Como.

We coo over the astonishing, impossibly decadent rooms. “It was amazing, those years, to be surrounded by so much beauty,” she says. “But, you know, life must go on, and I am very happy to have my memories.”

These days, Francesca divides her time between London and Milan (where her boyfriend lives — Tomaso, a banker). She runs with a pretty fancy set: one of her best friends is Barbara Berlusconi, Silvio’s daughter. The pair have started a charity to help some of Milan’s poorest kids. Ultimately, though, she sees herself returning to the family business full time. “I hope so,” she says, with an impressive lack of coyness. “If they’ll have me.” Surrounded by much luxury, yet hardly spoilt at all. Well, if you don’t count these student digs and their seven-figure price tag.

Times recommends

• Second homes: credit crunch casualty or money-spinner?
• How I built my own sliding house
• Top 10 incentives for house buyers