Polly Stenham’s play That Face left even London’s most codgerly critics struggling to stuff their reviews with enough superlatives. Aged just nineteen and having written only a single play, she found herself hailed as an important new voice in British drama. There were asinine congratulations for her on being so young and yet so interested in theatre, while those who had actually paid attention were deeply impressed by her gift for evoking pain and longing on stage with such sharpness and charisma.

Next month, with a West End run already completed and a film version of her play in the pipeline, That Face is coming to the Tron Theatre under the direction of Andy Arnold, in what could be Glasgow’s essential theatre event of the autumn.

There’s a son, there’s a mother, and there’s a big white bed on which, as Stenham says, ‘it all goes down’. It’s in, on and around this big white bed that volatile blood-ties are tested and torn, subjected to what Stenham calls the ‘blowtorch’ of theatre’s unblinking scrutiny. The family, she says, is her prime imaginative resource, and her work pries into close, taut relationships, taking their latent energy as the catalyst for dramatic action.

That Face has gained much attention for its handling of mental illness, but for Stenham this is far from a single-issue play. ‘It’s like seven different things to me. It’s a story about siblings, it’s a story about a mother and a son, and it’s a story about alcoholism and being bipolar. It’s a story about institutions. So there are a few paths through it, and a few ways of looking at it.’

Confronted by the play’s incisive and assured account of familial crisis, many critics have explained away Stenham’s virtuosity as the result of first-hand experiences in her own complicated background. But however heartfelt her writing appears, Stenham warns those who regard her plays as complex, confessional dramatic memoirs that they miss much by doing so. ‘I think, I watch, I listen,’ she says, ‘but my work is fiction.’

The idea that That Face might not just be by her, but is actually about her, irks Stenham mainly because her refreshingly ambitious conception of theatre is all about allowing performances to live unbothered by marginal figures like writers and directors. ‘I don’t go to the theatre to be told what to think,’ she says. ‘I go to see what I do think. Whatever the audience take, they take. It belongs to them, really. Once I’ve finished writing, and the director’s left the room and the lights come down, it’s them and the actors. Whatever they take from it is what it is. I’ve no desire to control their thoughts. Take what you want. Take nothing, take everything, it’s up to you.’

The thrill of going to watch a play, according to Stenham, is that it’s difficult and demanding. ‘It’s the storytelling form that honours the audience the most. It asks so much of you. It says, “Do go with us. Trust us. You’re bright enough to do it.” It doesn’t spoon-feed you like television does.

‘It’s mainly about people, and people with other people. It becomes a very human thing, which examines the state of us, right live in front of you. There is so little waste. It all comes from this fifty square feet of land; you just create this thing, and I think it’s wonderful.’

That Face, The Tron Theatre, Glasgow, Tue 6 Sep–Tue 20 Oct.