As Polly Stenham chatters in the basement bar of the Royal Court theatre — the edges of her public- school accent flattened, and her elfin body in a perpetual wriggle — she begins to scratch her nails into the arm of the brown leather sofa. She has no reason to be so nervous. Upstairs, her second play, Tusk Tusk, has opened to wild reviews, just as her first, That Face, did two years ago. But Stenham is still only 22, and acclaim, it seems, sits uneasily with her.

“I try not to read reviews, and I’m not getting carried away with what people say about me,” she insists, in her surprising alto. “You know, I’m very proud of what I’ve done, but to be honest with you, my main emotion is unbelievable relief. I was almost certain this play, which I worked on for 18 months, wasn’t going to go on. I stood outside the dress rehearsal crying, because I thought it was a complete piece of shit.”

Tusk Tusk is definitely not that. It is a gripping story of three middle-class siblings — Eliot, 15, Maggie, 14, and Finn, 7 — whose father is dead and whose bipolar mother has abandoned them again. Throughout the play, we only see the children in one room of their flat. The dread that their mother might have gone for good is tempered by the knowledge that if they call the police, Finn will be taken away by social services. How Eliot and Maggie solve this dilemma, and keep their own relationship intact, is the heart of the play.

It sounds bleak — it is — but the high drama is punctured with moments of rich, dark humour. Indeed, Tusk Tusk inhabits the same world as That Face, the piece Stenham wrote while in the first year of an English degree at University College London, aged 19, and which appeared at the Royal Court in 2007. (It is a measure of how far Stenham has risen in critical estimation that That Face is now studied in seminars at her former university.) Her first play also concerned a mother gone berserk, and public-school kids left to mop up the mess.

The general setting is understandable. Stenham is the elder of the two daughters of Anthony “Cob” Stenham, an arts patron and businessman credited with turning around the fortunes of Unilever, and the painter Anne O’Rawe. Cob looked after the girls when he and O’Rawe divorced, nine years ago, and Polly attended Wycombe Abbey and Rugby schools before taking a place at UCL — a course she left after a year, when That Face took off.

“I didn’t realise before That Face that writing about the middle classes so scathingly was quite a rare thing,” she says. “But there’s no mystery as to why I write from that perspective. I’m middle-class.”

There is, however, some mystery as to why she keeps returning to broken families — and, in particular, to mental illness. One critic suggested that Stenham is concealing “an unhealed private wound”. She would rather talk about “the work”.

“Yes, there are similarities between the two plays,” she says. “I’m fascinated by mental illness, riveted by it — it’s so sad and frightening and dangerous, and it has such profound implications. But I don’t know why you’re interested in the things you are.”

Does she have personal experience of mental illness?

“Yes, I mean, I’ve known people who have struggled with it,” she says. “Not necessarily people that close to me — other people's parents, for instance.”

Subject closed. For the record, Stenham says she is already working on her third play, which will be “much more fun, much bigger, a lot naughtier, a lot more malevolent. I feel like I’ve been very sincere up till now. It’s going to be about a group of friends — and that’s all I can tell you because that’s all I know”.

Her next commission for the Royal Court is not, however, the only thing on her mind. Under the tutelage of Pawel Pawlikowski (who made the acclaimed My Summer of Love, with Emily Blunt), she is writing the screenplay for That Face, has an open brief from Film4 to write “basically whatever I want”, and is also adapting the anonymously written novel Sabine for film. I know writers in their forties who would be happy with this kind of résumé. Stenham won’t be 23 until next year. Where has this creative juice come from?

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