Mixed Up North, Wilton's Music Hall, LondonThe Kreutzer Sonata, Gate, Notting Hill, London

Multi-cultural Burnley is viewed through the travails of a youth drama group, and a short story by Tolstoy gets a long-awaited staging, with a violin sonata at its heart

Uniting communities – healing wounds, harnessing the energy reclaimed from violence – is something the performing arts do well. In classical music, it's almost obligatory. Think of the artistic and political triumphs of the West-Eastern Divan Orchestra and its Palestinian and Israeli players, or the Simon Bolivar Youth Orchestra, its disadvantaged members liberated by Rachmaninov and the rumba. What better outlet, then, for rowdy, angry or terrified kids than a play – licence to be someone else, or your often unacceptable self?

In Mixed Up North, social worker Trish, played by Celia Imrie – "I'm a gateway to a lot of things" – is called by God to Burnley, after the riots of 2001, to bring together Asian and white youngsters who are fearful or suspicious of each other. Years on, the town is stuffed with youth and community workers, social workers, anything but workers plain and simple, since the loss of its textile industry to rivals overseas. Trish's contribution is StreetYY, a drama club made up of disaffected and damaged youngsters, leg-spreading youths and chippy girls, each with their own burden.

It hasn't been easy: white boys would rather drink, Asian boys think drama's gay, white girls risk being called paki-shaggers and Asian girls aren't allowed out. The few whom Trish does gather in go along with her earnest research into mixed relationships, although their own more vivid experience paints in an alternative landscape of knicker collections, phone videoing and cider-fuelled date rape.

The show opens with the dress rehearsal for StreetYY's latest play, a fraught and fractious occasion, dominated by impromptu basketball, tiffs, and failed attempts to introduce the concept of salad at sandwich time. As the run-through staggers to its feet, a key player walks out, and Mixed Up North takes a right-angle bend into a polemic on the politicisation of daily life, the grooming of white girls by influential Asians and the lure of the BNP.

Outstandingly cast and acted, Robert Soans's play is propelled across occasionally clumsy plot developments and writing by its youthful momentum. Most of the cast, including Lisa Kerr as slack-jawed dancer Kylie and Kashif Khan as foul-mouthed Sarfraz, are fresh out of drama school. Muzz Khan, as street-fighter Uday, tells a compelling tale of racial tension as, one by one, in Chorus Line style, the show's individuals reveal their scars: childhood abuse, parental neglect, drugs. As "guests" at this dress rehearsal, we listen in to the confessions – and are privy to the unfortunate moment when Imrie, on being told by a girl that she has been raped, casts down her eyes and says, "I knew it was serious," in a moment straight out of Acorn Antiques. Not her fault: the line is almost impossible to deliver.

Much of the ground in Mixed Up North was well covered by David Edgar in Playing With Fire in 2006, for the National Theatre, under whose umbrella this co-production by Out of Joint and the Octagon Theatre, Bolton, is being staged in London. But this new play, vigorously directed by Max Stafford-Clark, is going to raise these issues with a new, younger audience, if Wednesday's delighted young crowd is anything to judge by.

Enthusiastic pupils from Camden, north London, and Eton, Berkshire, were going head-to-head with the cast after that performance. An East End audience under 25 years old, the theatre's neighbours in fact, will be the most discerning critics of Mixed Up North, which should be in the diary of every local councillor, and every something-or-other worker.

Heaven knows where any social worker would start with Pozdnyshev, Leo Tolstoy's grotesque creation in his short story The Kreutzer Sonata, freely adapted by Nancy Harris and fulfilling the original author's aspiration that it would one day be staged with the Beethoven duet that is at its heart. Set on a rolling train, its relentless rhythm throbbing beneath the words, it is a monologue, delivered with chilling and virtuosic precision by Hilton McRae (below). The traveller's reptilean "glittering eyes", which Tolstoy comments on repeatedly, alight in the direction of the audience on an invisible fellow passenger to whom he reels out his sordid tale, in episodes at first disquieting, ultimately appalling, as elements of the Kreutzer sonata itself build tentatively off-stage. A few faltering bars on the piano, an exploratory violin arpeggio or two, are enough to suggest a connection between the man's wife (Sophie Scott) and old acquaintance Trukhachevski (Tobias Beer). As the music grows in confidence, so Pozdnyshev's remembered suspicions reach their murderous conclusion.

This miniature tour de force is gripping theatre, a poisonous extract distilled from Tolstoy's original creation and thrillingly performed. Where Mixed Up North teems with life, The Kreutzer Sonata simply seethes, horridly and compellingly too.

'Mixed Up North' (020-7452 3400), to 5 Dec; 'The Kreutzer Sonata' (020-7229 0706), to 5 Dec