As the bassist and co-vocalist of Sonic Youth, the New York art-rock outfit formed in 1981, Gordon is part of one of the most influential bands on the planet. But she’s much more besides. Model for Calvin Klein. Actress in Gus Van Sant’s dreamlike film Last Days (she played a sympathetic record-company executive). The woman who introduced Spike Jonze to Sofia Coppola and discovered Kurt Cobain. In the 1990s, she even had her own fashion range, X-Girl, a sister label to the Beastie Boys’s X-Large. Now, at 53, she’s the new muse for Marc Jacobs, whose born-again grunge look for this autumn is heavily influenced by her glamorously downbeat aesthetic.

Gordon is a 21st-century polymath and a walking, talking inspiration. She is emerging as a refreshing antidote to the vacuous lollipop girls — Nicole Richie, Paris Hilton and the like — who have come to dominate American pop culture. Just as Sonic Youth’s brand of dissonant rock has never been damaged by mainstream success, so Gordon herself has always skirted the margins of commercialism, happily doing her own thing. She did the whole grunge-goddess thing long before Courtney Love was even invented. It’s this independence of spirit that is winning her respect among the MP-She generation (the name given to the growing ranks of new female rock fans), and the reason the band’s first album, Sonic Youth, has just been re-released for a new audience. Sonic Youth T-shirts are one of the few bits of rock fashion memorabilia you don’t have to wear ironically.

As she picks at dim sum in the foyer of a coolly corporate London hotel, Gordon looks like Sofia Coppola’s older sister, or YSL muse Betty Catroux: feline eyes rimmed with grey eyeliner, dirty-blonde hair in an irregular bob, petrol-blue mac, saggy grey cotton top, T-bar dance shoes, Marc Jacobs white patent quilted handbag. At an age when most women are sinking happily into late middle age and elasticated pants, she is clearly still rocking out. I wonder what keeps her feeling young and relevant. “Topshop!” she laughs. You have to say it, she looks amazing for her age — no Botox, no fillers, no face lift, no dermatologist on speed dial. “I don’t make that much money,” she says. “I just hope my good bones will take me through.”

The daughter of a sociologist father and a seamstress mother, Gordon attended art college in Santa Monica, Toronto and LA (“I wasn’t a good student”) before moving to New York in 1979. By day, she painted; at night, she went to loft parties in downtown Manhattan and SoHo, and watched bands at seminal rock and punk hang-outs such as the Mudd Club, Danceteria and CBGBs. “Everybody seemed to be making music for the sheer pleasure of it,” she recalls. In those days, Gordon was a brunette with a sharp fringe and large spectacles. She played in the female trio CKM before hooking up with her future bandmate and husband, Thurston Moore. “We met through a mutual friend who we were both making music with,” she says. “She thought we would hit it off.” They did, and, after a few all-night conversations, Sonic Youth was born.

That was 25 years ago, but Gordon’s style remains undiminished. Are there any rules to dressing as a 50-year-old? “I don’t know,” she admits, in her quietly spoken way. “Whenever I look in those fashion magazines that have sections on what you should wear when you’re 20, 30, 40 and so on, I never really like what they have for the 50-year-olds. I always prefer what they have for the 30-year-olds. I think you have to think about your personality and what you identify with as you get older.”

She’s remarkably easy-going and humble, this rock chick’s rock chick. I ask her what she thinks that is. “I always think it’s Chrissie Hynde or someone like that,” she says disingenuously. “The perfect rock chick is a contradiction in terms, because part of the appeal of being cool is that you make it look easy. The clothes have to look like you’ve worn them every day on tour for a month. I always want to do the opposite of what you’re meant to. There’s something about wearing a dress on stage that makes me vulnerable. It’s more interesting than wearing black leather and looking all hard — that’s not as risky, somehow.”

So, what does it take to rebel these days? “I think the reason someone like Chloë Sevigny is singled out as fashion-forward is because a lot of her style isn’t overtly sexy or Hollywood, it’s more to do with gesture. She doesn’t wear her sexuality on her sleeve. Some things might even look conservative and dowdy. She plays on that. Because a lot of the people who look outrageous are actually very conservative underneath.” Like Paris Hilton? “ Yeah, exactly.”

Gordon is an incisive observer of the bubble-gum world of celebrity. On a recent tour, she gave an ironic shout out to Jordan. She has also penned a song about Mariah Carey’s breakdown, and famously wrote Tunic, a thrashy paean to the anorexic, treacle-voiced Karen Carpenter. “Observing those celebrities is just an idle pastime,” she says. “They’re part of our landscape. We don’t have history in the USA: we have Hollywood, we have pop culture. For us, it’s like looking at nature.”

At this point, Gordon’s 12-year-old daughter, Coco, strolls into the hotel and slumps on a chair next to us. She has a curtain of honey-blonde hair and her dad’s puppyish facial features. She’s sighing, a picture of ennui, all too familiar with her parents’ itinerant lifestyle — hanging out in hotels, being interviewed, sound-checking gigs. “She’s at the age where she wants to wear one thing and wear it every day,” says Gordon. “She’s definitely a cool kid, the way she dresses. Her and her friends, they really frown on girls who wear their skirts too short — and they’re really down on Lindsay Lohan.”

Somehow, you expect nothing less. No obvious teen idols for the daughter of the original grunge icon. Just like her mother, she’d rather go her own way.

Sonic Youth’s new album, Rather Ripped, is out on June 5 (Geffen); Sonic Youth by Sonic Youth (Geffen) is out now

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