Jaime Winstone is living it large. She has beaten up a giant purple gorilla, fallen in love with a gay Buddhist kung fu monk, and pulled out a hefty tranquilliser gun from a pair of magic hot pants. And that's just the beginning. For, as Whitey Action, the high-kicking teen protagonist of the celebrity-bashing satire Phoo Action, the 22-year-old firebrand actress has found in her angry wild-child character a kindred spirit of sorts. “In the real world you can't go round pulling tranquilliser guns out of your pants, though I wish I could,” she says, her brown eyes bright with enthusiasm, her slight, pixie-like frame leaning forward on a large armchair in the corner of a swish Central London agency. “But Whitey is an anarchist in a modern day world who's fighting the pressures of bullshit celebrityism, so in a way I can relate to that.”

Whitey, she explains, was initially conceived by the Brit-comic guru Jamie Hewlett (Tank Girl, Gorillaz) as a punk sidekick to the martial arts monk Terry Phoo in a mid-1990s comic strip called Get The Freebies. The strip, which ran in the now defunct style magazine The Face, was Hewlett's action-packed Technicolor broadside against the celebrity obsessions that seemed to be strangling popular culture at the time, but were actually, in hindsight, only in their infancy (Big Brother began four years after the Freebies appeared). It's hardly surprising then, says Winstone, that the Freebies adaptation Phoo Action, which is set in London in 2012 and features a grim dystopia where celebrity mutants are controlling the world, should now be more stingingly relevant than ever.

“It's going to be shocking and controversial for some people,” she says, obliquely. “A lot of it relates to certain characters who are in the public eye, and they are targeted in a funny, edgy way.” She adds, of course, that the show, an hour- long feature, whole and complete in its own right, but crying out for a follow-on series, will be wildly entertaining as well. “It's like a trip without the acid, it's experimental, it's brave and it's risqué. There's been nothing on TV like it since The Young Ones.”

And yet, you suspect that part of the appeal of playing Whitey Action is the chance that it gives Winstone, the daughter of the iconic actor Ray and currently dating Alfie (brother of Lily) Allen, to vent some spleen at the prurient celebrity culture that increasingly surrounds her, and her relationship with Allen, in particular.

“For a start, it's weird to be even called a celebrity, because I'm not,” she says. “And it's completely unnatural to get a new boyfriend and for it, suddenly, to be like: ‘They're gonna get marred! They're this! And they're that!' You just have to take all that stuff on the chin and not give in. Because the moment you let it get to you is the moment you've bought into it.”

Winstone adds that she wants her work, and not her celebrity, to define her. Which is good, because she's currently building an admirable back catalogue of leftfield turns. As the slatternly loudmouth Becky, for instance, she was the best thing in Kidulthood, brazenly louche and naturalistic on camera when those around her seemed stiff and unsure. Her beguiling combination of elfin features and ineffable toughness has made her the go-to girl for hipster promo directors, and she has starred in videos for the Streets (When You Wasn't Famous), the Twang (The Lovers) and, most recently, for the New York rockers Hercules & Love Affair (their Blind promo features Winstone, in eery close-up, drifting slowly through an art-designed orgy. “Promo directors are really intense, and they don't want just this pretty little thing,” she says. “They want a performance from you, and that's what I give them.”

Winstone's movie work will continue this year with the thriller Donkey Punch and the star-splashed ensemble Boogie Woogie. The former flick, a re-imagined slasher film set aboard a yacht, was an audience favourite at this year's Sundance Film Festival. The title refers to an unmentionable sex act that goes badly awry and eventually transforms a party cruise into a paranoid blood bath. “We shot it over 24 days in South Africa,” says Winstone. “We were covered in blood and crying for three weeks solid. It was draining, but it was such a buzz.” Boogie Woogie, on the other hand, is a sophisticated character piece about London's art world, and features Winstone as a self-described lipstick lesbian sharing screen space with heavyweights such as Heather Graham, Danny Huston and Christopher Lee. She says that, luckily, she never gets star struck because she's grown up around her father's fame. “I've been on Scorsese sets where you watch in awe,” she says. “But you realise that it works exactly the same as a short film in Liverpool or Newcastle.”

She says that she shoots short films in her spare time, that her relationship with Allen blossomed “naturally and organically” (they met on the set of Boogie Woogie, where he played a photographer), and that ultimately her mission is to achieve longevity in this most precarious of careers. “I think that the media want to put you up on a table just so they can kick you off it again,” she says. “I'm in no rush to become extremely famous, or to have status. I just want to continue being an actress.” She allows herself a baffled blink of her deep brown eyes, and adds, “In fact, I don't think I want to get onto the table at all!”

Phoo Action is on Tues, BBC3, 9pm

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