Poliakoff Jr, talking about her generation

Laura, daughter of top British dramatist Stephen, shows she has a voice all of her own with her debut play. By Alice Jones

Stairway to fame: Laura Poliakoff, whose new play, 'Clockwise', premieres at the High Tide Festival (Ki Price)

Let's start with the similarities. They share the same surname, obviously. And quite a lot of genetic material. And they're both writers. Apart from that, Stephen and Laura Poliakoff don't appear to have a lot in common. As Stephen, 59, puts the final touches to his first BBC TV series, Dancing on the Edge, a typically sumptuous period affair following the fortunes of a black jazz band in 1930s London, his daughter, 27, is preparing to bring her first play – a sweary, dystopian black comedy set in an old people's home in 2065 – to the stage.

Poliakoff Jr, a history graduate, started out as a researcher on her father's period dramas. "I just trawled through loads of history books and biographies. I know what my Dad's looking for – the juicy, real-life stories that he can incorporate into his script, which aren't just facts," she says. Most recently, she worked on Dancing on the Edge, spending several days on set. "I love the period and the music. It's set in 1933 or 1937. Probably 1933. Oh God, this is embarrassing... It's set in the 1930s."

It's all in the past now anyway, as Poliakoff launches a career in her own right. Having left the National Film and Theatre School just over a year ago, tomorrow she will premiere her first play, Clockwork, at HighTide, the Suffolk theatre festival for new writing, whose patrons include David Hare.

The play is set some 50 years in the future in a care home staffed by hoodlum teenagers and clock-watching nurses. Its antiheroes are Carl and Mikey, best friends since childhood, now in their seventies and still wearing adidas and listening to grime. Grumpy, filthy, foul-mouthed, these days their only kicks come from popping pills to the Archers theme tune and hiding porn and cigarettes under their wheelchairs.

"I just liked the idea of imagining my generation as older people. It's quite hard when you talk to your grandparents or go to visit a care home to imagine that everyone in there was a teenager once and that they could have led the most exciting or debauched lives," says Poliakoff. "I thought it would be an interesting way of looking at old age."

The play also makes a serious point about ageing populations and how society cares for its elderly. Poliakoff's dark vision includes 500,000 centenarians on the loose, a crime wave caused by poverty-stricken pensioners, and Alzheimer's patients having memory chips implanted.

Putting the concerns and vernacular of her peers into the mouths of ageing actors is the kind of witty, eye-catching trick that is bound to see Poliakoff hailed as the next big Young Female Playwright. Reminiscent of an early-era Amy Winehouse with her hoop earrings, lashings of eyeliner and dyed hair, she looks the part. Laconic and witty, with a feisty way with words, she sounds it, too. At HighTide, Clockwork will run in rep with new plays by similar hot properties Ella Hickson, Vicky Donoghue and Stephanie Street, and Poliakoff is enrolled on the Royal Court's starmaking Young Writers' Programme whose alumni include Polly Stenham and Lucy Prebble.

Writing is, of course, in Poliakoff's blood. Her father is a prolific purveyor of plays and classy TV dramas such as Shooting the Past and Friends and Crocodiles. Her mother, Sandy Welch, is a scriptwriter whose adaptations for the BBC include a Bafta-winning Our Mutual Friend (1999) and an Emmy-nominated Jane Eyre (2007). She grew up in Angel, north London, with her younger brother, Alex, and went to the all-girls Francis Holland School. Occasional set visits aside, her childhood wasn't the whirl of beautiful people and glamorous parties seen in her father's dramas.

"My parents are quite private people. There weren't actors, directors and other arty people coming through the door every five minutes," she says. "They'd both go off into separate rooms and work for hours. My dad's room was always covered in scripts because he wrote everything by hand. Still does. He thinks that it forces you to think more about exactly the sentence you are writing if you can't just, you know, write a load of old shit, delete it and edit it. And he's right."

She began writing as a child. "Terrible, terrible things. My dad would be working towards an important deadline and I'd shove my awful pages in front of his face and he'd say things like, 'Hmm, maybe if you reach the end, we'll have a clearer idea of where that was going.' But he was always encouraging." Her departure for university in Bristol inspired its own TV drama, Gideon's Daughter, about a widowed father (played by Bill Nighy) coming to terms with his distant daughter (Emily Blunt) flying the nest.

After graduating, Poliakoff moved back into her childhood home – where she lives with friends while her parents try to sell it – and enrolled at film school. There she started writing in earnest and discovered a talent for witty, twisted tales. Bertie Crisp, a short animation about a put-upon bear and his psychopathic rabbit wife, voiced by Tamsin Greig and Kathy Burke, recently won a British Animation Award. Other coursework included Prude, a short film about sexual awakening set in Loch Ness, and a play in which a couple bicker about chlamydia. "I never wrote about female sexuality in order to make a political statement but people have been strangely surprised. 'Oh, you're a woman and you're writing about the fact that women want to have sex'. It shouldn't be a weird thing, but it is."

She's now writing an episode of Doctors – "first proper credit for the Beeb" and has been commissioned to adapt Elizabeth Ridley's novel The Remarkable Journey of Miss Tranby Quirke, about a lesbian affair between a repressed teacher and her student.

Growing up in a writers' household, she says, has taught her the importance of originality and being prepared for criticism. So does she think her surname will be a curse or blessing in future? "I don't think it's going to be a curse but I guess people will be intrigued to see whether I'm terrible or not."

'Clockwork', High Tide Festival, Halesworth, Suffolk (hightide.org.uk) 4 to 13 May