Von Furstenberg's signature wrap dress sits in the Smithsonian Institute, yet is still dressing women today. Next year, it turns 40

When I meet Diane von Furstenberg, she's writhing on a white leather sofa, serving double-duty as a postmodern banquette, one hand toying with the buttons at the neck of her dress, the other plunged deep into a curled mane of hair, tugging it horizontally from her taut cheekbones like those Jerry Hall Opium adverts.

Hovering in the background are a few dozen Warholian red lips, chicken-pocking an otherwise pristine wall. They're not a mirage, or indeed an LSD- induced hallucination. We're sat in the London offices of Diane von Furstenberg – the woman, and the label – atop her eponymous boutique on Bruton Street. The lips are hers. And they're Warhol's, too. They are from one of her very many portraits by him, the ones she snapped up for a song after he died. The one she didn't, she says, is in the Philadelphia Museum. You can take the girl out of Studio 54, but you can't take the Studio 54 out of the girl.

You expect this of Diane von Furstenberg. That's the wrong turn of phrase: you don't expect it, so much as hope for it. She is after all, the Princess Diane von Furstenberg, European party girl, Seventies disco diva and bona fide fashion icon – in the true meaning of that much-overused phrase. She ran up some frocks while pregnant and showed them to legendary American Vogue editor Diana Vreeland, who pronounced them "smashing" and put them in her magazine. That was in 1970. A career was born. The dresses she ran up ended up in the Smithsonian Institution, as well as on the backs of scores of revellers at Studio 54, Von Furstenberg's hangout of choice.

It's also all accidental, or at least it is the way Von Furstenberg tells it. "The first time I sat on the cube," she points to the famous 1972 advertising image of her astride a white box, hair flowing, dress concealing and revealing, the epitome of the confident, modern, fashionable woman of the Seventies, "is because I couldn't afford marble and so I sat on the cube. I wanted to run the ad and the cube was too big – this big white thing – and so I said 'I should write something on it'. So I just wrote 'Feel like a woman, wear a dress' and signed my name. Not thinking all of it would stick to me. It just happened! It's not like I designed it that way." Which, you suspect, is part of the legend of the legendary Diane von Furstenberg. She could have come straight from central casting – she's so aware of the role she's playing. The sexy designer of sexy dresses that helped sex-up the sexual revolution.

The sexiest of Diane von Furstenberg's dresses was the wrap dress. It's a simple thing – a jersey dress that wraps around the figure, tying with a fabric belt. Sounds standard today, but 40 years ago no one had done it. That's the dress that ended up in the Smithsonian, after netting her millions – $150 million in 1979 alone – and winning legions of fans. What's it all down to? According to Von Furstenberg, sex. "I used to say always that you can get in and out making no noise," she moans, dragging out the sinuous, serpentine 'ess' until it's at least three hours long. "It's four in the morning, and he's sleeping and you're going home… you go very low, you put the dress on, you make no noise…" She's painting a scene straight out of Last Tango in Paris.

Von Furstenberg's autumn/winter 2013 collection

Diane von Furstenberg is 66. She pronounces it "sexty-sex". You'd never guess – the age, I mean, not the pronunciation. She crosses and uncrosses her legs like Sharon Stone in Basic Instinct, then leaps off the leather sofa and prowls the length of her showroom, hung with rails of her latest collections, like a caged tigress, pawing the fabrics. "Body language is for me the most important thing," she purrs softly, eyelashes batting as she intones mantra after mantra: "Effortless, sexy, on-the-go!" She caresses a dress: "Flirt with my body!" It's a captivating, caricatured performance. This sex-kitten has us smitten.

In case you haven't fathomed, Diane von Furstenberg is her own best advertisement. She's a billboard for her brand, its physical embodiment, her own muse and figurehead. That's because the brand, ultimately, is all about her. It's almost always abbreviated to DVF, as is she. And those lips, her lips, are an emblem of the label. Its logo is her signature. She starred in the early advertisements. It sounds rather personal, but everything about her label is personal. She's still at the helm of it, despite a few blips and flips along the way.

DVF (the woman) lost control of DVF (the label) in the Eighties, and tussled for much of the Nineties to regain control. "It was hard," she says of that process. "It was hard to take it back and to see it all fall apart. But they paid me a lot of money! So I went to Paris for a while and when I came back I realised what had happened and then I tried, and gradually got it back... you eat humble pie, and then you move on."

The latest blip was Yvan Mispelaere, a Frenchman who was creative director alongside von Furstenberg for two years, exiting shortly after her spring 2013 show. 'Blip' is perhaps a cruel dismissal: prior to Mispelaere, she worked alongside designer Nathan Jenden. But now she's running the show, literally, figuratively and happily, as both head designer and co-chair. She's also president of the Council of Fashion Designers of America. In her free time – apparently, she still has some left – Von Furstenberg likes to hike at Cloudwalk, her 100-acre country farm in Litchfield County, Connecticut. She's also writing a book called, tentatively, The Woman I Wanted to Be. She does a good line in titles. Back in 1979, she published Diane von Furstenberg's Book of Beauty: How to Become a More Attractive, Confident and Sensual Woman. That's a hell of a mouthful.

The obvious question today is: who is the woman DVF wanted to be? Von Furstenberg sighs. The hand goes into the Jerry Hall hair. And she begins. "I actually became the woman I wanted to be really early on," she says, carefully. "I wanted to be independent, I wanted to be able to pay my bills, I wanted to be able to have a man's life in a woman's body, I wanted to be able to be... free." She glances over, checks I'm listening. "Clearly, in order to be independent you've got be financially independent. And I became the woman I want to be through fashion. Because the door of fashion is the door that opened to me. I did not know," an eyebrow arches, she glances again. "It's not like I wanted to go into fashion. It's that I wanted to become that woman, and the door that led me to be that woman was fashion."

Then, Von Furstenberg maps out exactly how. Her ability to package 30 years into a 30-second nutshell is astonishing, a feat honed through years of interviews – interviews where she's probably been asked questions very much like mine. Von Furstenberg began working with Angelo Ferretti, a manufacturer of scarves "for Ferragamo and Gucci, people like that". She convinced him to let her run up some dresses. She was young, pregnant and engaged to a scion of European aristocracy, Egon von Furstenberg. They divorced in 1972, but even before they married Diane had a thirst for her own independence.

"I went to this man [Ferretti] and said listen, I'm pregnant, I'm eng...'." She stops, reconsiders. There's a better way to paint the legend. "'I'm getting married in a month and a half and I'm moving to America, can I make the samples from your factories?' So that was it, that door opened and I made a few dresses. And then I came to New York and I went to see Diana Vreeland, she loved what I had and from there it... you know." A star is born.

Von Furstenberg with model Coco Rocha backstage at her New York fashion show (Getty Images)

It's evidently a story Von Furstenberg has told a million times – not least in her 1998 book, A Signature Life. Her autobiography is great. It reminds me of Marlene Dietrich's fabulous, self-serving memoirs, where she jumbles history and slipstreams her birthdate about flatteringly. Incidentally, DVF is a Dietrich fan: "My style heroine is Marlene Dietrich," she declares. "I love her." There's also a touch of DVF's early supporter, Vreeland – an avowed champion of 'faction' over fact. A Signature Life is filled with glamorous pictures of DVF sprawled across glamorous apartments with her glamorous friends, and anecdotes written in glamorously large font to use reams of paper.

Glamour, really, is what Von Furstenberg is all about. Back in the Seventies, it certainly helped to shift those wrap dresses – you weren't just buying a frock, you were buying Diane von Furstenberg, and every slither of cotton-rayon was somehow lassoing you to the tabloid-worthy glamour she called her everyday life. It's still the case today.

The DVF label was revived in 1997, while Tom Ford was catapulting Gucci to new currency by referencing the Studio 54 hedonism that Von Furstenberg had partied through first-time round. Her vintage pieces were doing swift business, and influencing younger designers. Unlike so many of her contemporaries – Halston, say, or Giorgio di Sant' Angelo – DVF herself could still offer consumers a slice of the real deal. Which is why Madonna, Gwyneth and a whole host of fashionable women pounced on Von Furstenberg's reissued wrap. In September 1997, she relaunched the label: Scoop, a New York boutique, sold out of their consignment within half an hour. It was a museum piece that, ironically, could still be worn by everyone.

The wrap dress hits 40 next year – marked, fittingly enough, with a collaboration between Diane von Furstenberg and the Andy Warhol Foundation on a series of prints for said garments – and there's still a healthy market for that indefinable, indistinguishable Seventies jet-set glamour that's synonymous with DVF.

"I love glamour," growls Von Furstenberg. "It's funny because I'm writing a book right now and the woman I work with, she keeps saying, 'Well we have to find another word than glamour!' and I said, 'There is no word! I like the word glamour!'." Does she see it as part of her job to be glamorous, then? After all, DVF is... well, DVF. She's her own brand, and as such she's expected to be out representing, looking polished and poised, pressing the flesh. "No," DVF demurs. "If anything it's not a part of my job, it's part of..." You? A feline grin uncurls from cheekbone to cheekbone. "Yes. I always wanted to be glamorous. When I was a little girl. Glamour is super-important." But is she ever worried all that glamour overshadows the hard work – at least, in other people's eyes? The grin doesn't subside. It widens, even. "That's a good thing, no?"

Despite the lure of glamour, according to her, fashion wasn't young Diane's choice of career. "Growing up I was interested in literature more than anything. But then when I asked somebody, 'What can you do if you like books?', they said you could be a librarian. The librarian in my school had big thick glasses and bad breath... and I didn't think I want to be a librarian." Instead, she married a prince, moved to New York and dressed the world. A clear win for glamour.

But is it a clear win for Diane herself? Despite her fame and success – considerable, running at four decades and counting – there's the feeling that fashion, and her perceived position inside it, rankles her. "You know fashion is a very mysterious thing, because it is the reflection of your time yet when you live it you don't... sometimes you think something is so important but it passes and you forget about it," she says in a measured voice. "Nobody ever thought that my dress would be important, even though I made 25,000 a week very quickly. Nobody paid very much attention to it. I got acclaim and this and that... yet if you think about it people say, 'Well she's not really a designer'. The truth is, I made a dress that was immortal." She pouts, raises an eyebrow, drinks. The legend has spoken.