Fashion favourite: Daisy Lowe's grungy glamour makes her a natural choice for the iconic fashion house Biba

When Daisy Lowe arrives for our interview wearing a long leopard-print coat from the new Biba collection, I assume she's chosen to wear it deliberately in her capacity as the new face of the label. After a vehement denial, and declaration that, "I've been wearing it the whole time, I wore it for Glastonbury with different coloured wigs", the 21-year-old model starts scrolling through her phone for photographic evidence from the festival.

Her explanation – "I like playing with clothes" – isn't strictly necessary. Even when she's not in festival mode, her style has an obviously experimental, playful exuberance to it. The naturally beautiful Lowe just doesn't look like the kind of girl who lays out matching outfits on her bed, agonising over whether she has any unladdered tights in the drawer. In fact, the tights she's wearing today – with a smock dress and workman's boots – are so holey that she's put knee socks over the top for a rebellious schoolgirl effect.

It's Lowe's grungy brand of glamour that makes her a natural choice for a label that epitomised youthful self-expression in its heyday. Ever since Barbara Hulanicki opened the first Biba boutique in London's Kensington in 1964 and made young, hip fashion more widely available, the label has had a mythological aura. An Aladdin's den, it attracted the bright young things of the Sixties and Seventies including the Stones, the Beatles, Marianne Faithfull and Bianca Jagger. And when "Big Biba" opened in 1973, it was one of the first "lifestyle stores", with six floors of fashion and accessories, cosmetics, food, furniture, and more.

Biba's nostalgic appeal is so strong that this isn't the first time its been reinvented since it closed in 1975 and the name was sold in 1977. This most recent revival is by the department store House of Fraser, which bought the label last year. It will launch the new line into 35 of its stores from 8 September – 10 of which will have special retro Biba boutiques – and it will also be available online at

Designed by an in-house team, House of Fraser's first Biba collection draws on the original label's flamboyance with a "luxe" theme, featuring faux fur coats, marabou jackets and limited-edition evening dresses alongside tailored coats and blazers, denim, and jewellery featuring the iconic logo.

The vision of the label is more opulent than the girlish collections Bella Freud designed for the brand when Michael Pearce bought it in 2006. However, given that Pearce's incarnation lasted only two years, and that the latest version of Ossie Clark, another cult Sixties label, closed last year, it could be a risky enterprise.

The difference this time round is that it's a retail project rather than a designer one, and it's much less expensive, with a coat at £290. It's "aspirational but accessible," according to Stephanie Chen, the executive director of womenswear.

Does Lowe think it will work? "Let me say, I hope so," she says with a surprising level of realism. "I think because there are boutiques, it will really bring people back. There are brilliant pieces – the coats are amazing and there's this beautiful butterfly ring that goes over two fingers."

Lowe wanted to be the face of the Biba campaign because she "loves the history of it". She even did a project on the label for her art A-level, for which she sketched "all the old interiors of the shops and stuff" (she went to the private South Hampstead High School in London, and proudly points out that she was predicted three As in art, chemistry and economics and a C in maths before she dropped out to pursue modelling). "I think I was just meant to be born at that time anyway," she says. "I kind of feel stuck in the late-Sixties and early-Seventies." She has numerous archive pieces from Biba, including pussy-bow shirts and dresses, and says that hunting for vintage Biba was a big part of both her and her mother's love for clothes.

Daisy's mum – Pearl Lowe, a former singer with the indie band Powder, one-time member of Kate Moss's Primrose Hill set and now a dress designer – is of course part of the reason she became famous in the first place.

Lowe says that as a teenager she was in awe of her mother's dress sense. She recalls that her mum "would never be caught dead without stilettos, she was just so hot. It was like, 'Oh no, I don't want to introduce you to all my friends ...' " Lowe maintains that her own teenage look was an "awkward" one, and that she didn't discover a signature aesthetic until she was 15. Her mum would bring home bags of clothes, and it was the Vivienne Westwood pieces in particular that fascinated Lowe. She's achieved her goal of modelling for the designer several times now – having appeared in Westwood's Red Label catwalk shows (as did fellow models and scenesters Alexa Chung, Pixie Geldof and Alice Delall, with whom Lowe's often pictured partying).

Lowe isn't a typical fashion model – instead of the skinny, Bambi-like vulnerability of most catwalk waifs, Lowe's rare slim-with-curves shape has an earthy, accessible sex appeal to it. She's excited that the fashion industry is starting to embrace curvier figures and – to her horror – was moved to tears by the voluptuous models at the autumn/winter Louis Vuitton show. "I started tearing and it was probably the most embarrassing thing I've ever done," she says. " I was thinking, 'Do not tear at a fashion show Daisy, it's not a play, you're just watching clothes'. But there were actually breasts in it, and it was celebrating women."

Lowe also differs from most models because of her status as a "personality", a term that, for once, isn't heavily ironic; she is intelligent, sparky and sweet. Her personal life has been documented like a soap opera by the tabloids; hardly surprising, given its dramas. One-time drug user Pearl Lowe had Daisy when she was 18, and Daisy only discovered in 2004 that the Bush singer Gavin Rossdale was not her godfather, as she'd been led to believe, but her father. Initially, Rossdale, who also hadn't known he was Daisy's father, severed all ties, but now the two families are on "good terms". Then there are her boyfriends: Blondelle singer Will Cameron, the music producer Mark Ronson, and current squeeze Matt Smith, aka Doctor Who.

She's philosophical about the interest in her private life: "I grew up in the public eye from the age of 15 and it wasn't a choice I made, it just kind of got imposed on me because of who my dad is. But one strange side-effect is the funny, weird, made-up stories that have no meaning whatsoever." Lowe explains: "Apparently I played a Gram Parsons song to serenade Matt, but I can't play the guitar and I only know three chords, so how does that work?"

She is often accosted by teenage girls for photos and autographs. Unlike the elusive Kate Moss, Lowe is an accessible figure, regularly communicating via Twitter. Unselfconscious and chatty, she's not one to keep her opinions to herself, especially when it comes to fashion.

On the shoot for the Biba campaign she says she was pleading with people from the label to "please, please make some pussy bow shirts, in any prints. Just make sure you do them because they are so flattering and feminine". Did they ask for her creative input? "No I'm just giving it anyway." Listen up Biba, you've got a free creative consultant on board.