The Sugar Syndrome, Theatre Upstairs, Royal Court, London

Who would you wish as a friend for a chippy 17-year-old girl with a history of chronic bulimia, a bad reputation for truancy from college and an angrily embattled attitude to her estranged parents? There aren't many people who'd suggest that a balding, middle-aged, unemployable paedophile with a prison record for molesting small boys would fit the bill here. But that's the deal in The Sugar Syndrome, a remarkably assured, funny and perceptive debut play by the 22-year-old Lucy Prebble.

The encounter between this oddly supported couple comes about courtesy of one of those online deceits dramatised by Patrick Marber in Closer. The mischievous and androgynously named Dani finds herself in a chat room with Tim and does nothing to disabuse him of the assumption that she is an 11-year-old boy badly in need of friends after a change of school. Pruriently fascinated, she even turns up to the playground assignation, planning just to walk past but not able to resist initiating a dialogue. Each both is and is not a disappointment to the other. She'd been expecting a freakshow dirty old man and instead is confronted by a posh, intelligent former classics teacher in his late thirties. He had been hoping for a prepubertal male and, once he's convinced that this is not a stitch-up, confesses he's rather relieved that Dani is not the answer to his fantasy. Mutually intrigued, they progress from being a partial let-down to each other to being a peculiar form of support.

There's an inherent risk of sentimentality in plays that depict the attraction of incongruous types bonded by their outsider status. Prebble largely avoids this in a drama that refreshingly refuses either to rush to judgement or to wield a brush dripping with whitewash. If she valuably humanises Tim - portrayed in an excellent study of wary wit and self-mistrusting irony by Andrew Woodall - she does not forget that he is by no means the main victim of his compulsions. The play is alert to the various grim and grotesquely comic paradoxes of his position: after a background-check, he was held to be unsuitable to teach an adult education class ("I mean... by definition!"); instead of curing him, a course of aversion therapy "made [him] want to electrocute kids".

It also helps you appreciate why Tim, with his outcast's candour, would feel like a sudden soulmate to a damaged girl such as Dani, a tricky tease whose surface sexual knowingness, underlying vulnerability and instinctive generosity are superbly caught in Stephanie Leonidas's eye - and heart-catching performance. It's not as if she derives much emotional sustenance from her fraught mother (Kate Duchene), a woman whose idea of self-assertion is to cut out the crotches from the suits her adulterous husband no longer wears; or from her geeky friend Lewis (Will Ash) who is all premature ejaculation and futile hopes of working for NME.

But there's a crucial scene at the end where Dani switches on the laptop that Tim, who wants to be led out of temptation, has given her to destroy along with her equivalent charged object - a tattered home-made "Thinspiration" scrap book, a bulimiac's bible of celebrity and fashion shots.

Throughout Marianne Elliot's vibrant production, there has been the recurring image of faces bathed in the ghostly radiance of computer screens, building up a picture of contemporary society as a conglomeration of web-addicted atomised loners. In this final tableau, we watch as Dani bears appalled witness to the rape of an eight-year-old, screaming for the ordeal to stop. Some may feel that this acknowledgement was tardy in coming, but I think its shock is shockingly well-timed in a humane and deeply promising play.

To 15 Nov (020-7565 5000)