Punk Rock, Lyric Hammersmith, London

Simon Stephens' powerful and compelling new play – which signals a new Lyric Hammersmith regime under Sean Holmes – does not quite deliver what it says on the tin. It's set in an old, traditional library in a fee-paying grammar school in Stockport and the music by Big Black, the Cows and White Stripes is only punctuation between scenes.

That is probably the point, or comma. The pupils are sixth formers sitting their mock A-level exams, and their number is joined by Jessica Raine's disturbing, self-harming Lilly, on whom the Hamlet of the reform, Tom Sturridge's blinking, oddly hair-styled William, immediately fixes.

Stephens is reunited here with his Manchester Royal Exchange director, Sarah Frankcom, with whom he brought his award-winning On the Shore of the Wide Wide World to the National four years ago; it's a dynamic partnership, and this brilliantly cast and acted play proves both a remarkable link with the Lyric's musical premiere of Spring Awakening last year and a mission statement of upcoming work for and about young people.

As in the Wedekind play and musical, we see middle-class pupils under peer pressure embroiled in sexual chess-playing and adolescent crisis with ultimately tragic consequences.

It's no accident that the Columbine High School massacre (echoed on our own doorstep the other week) also centred round a library, a terrifying update on the tradition of school plays stretching from Barry Reckord's Skyvers at the bottom of the education heap to Julian Mitchell's Another Country or Alan Bennett's The History Boys on the brink of future success.

These were not the happiest days of anyone's life, and it's a lovely coincidence that Tom Sturridge's father, the director Charles Sturridge, made his acting debut in Lindsay Anderson's If..., the first film to prophesy the sort of nightmarish scenario almost commonplace on school and college campuses these days.

Young Sturridge makes an astonishingly assured stage debut as a slightly more neurasthenic Ben Whishaw type, with a bob of unruly hair, a gangling physical expressiveness, a deliberately shaky grasp of his own domestic orientation – one minute he's an orphan, the next the son of a thriving oil millionaire – and a neat way of knowing that he's "the cleverest and funniest person in Stockport."

The other sixth-formers, kitted out in blue blazers and grey slacks or skirts, include the regulation Steerforth school bully, Bennett (done with a wonderful ambiguous coldness by Henry Lloyd-Hughes), whose campaign of belittling sexual taunting is rebuffed by Harry McEntire's Chadwick, the class swot, with a dazzling rhetorical speech of apocalyptic prophecy that destroys his opponent and wins a round.

Lilly's arrival is the axis on which the play turns, and Stephens' sly way of stretching the time span allows for a development of relationships within the group that prosecutes the outcome as the exams loom larger. Settling in, Lilly is drawn to the sexually charismatic figure of the blond muscleman Nicholas – another remarkable stage debut, by Nicholas Banks – while Tanya Gleason's friendly Tanya and Sophie Wu's hard-edged Cissy stir the pot by behaving just as you'd expect them to.

Stephens sounds few false notes in giving all of these kids great dialogue and solo riffs, though I did wince at Lilly's speech about most young people living decent and admirable lives – she started to sound horribly like David Cameron – but I concede that the playwright, an associate director to Holmes at the Lyric, is passionately committed to young people's theatre. Good for him, and for Holmes, and a great start to the new Lyric campaign.

To 26 September (0871 221 1729; www.lyric.co.uk)