Chariots of Fire, Hampstead Theatre, London Children's Children, Almeida, London In the Next Room (The Vibrator Play), Ustinov Studio, Bath

Adapted from the award-winning film, Edward Hall's staging of Chariots of Fire is just out of the starting blocks at Hampstead. Yet this homage to Harold Abrahams and Eric Liddell – Britain's triumphant Olympic sprinters of 1924 – already has a West End transfer confirmed for mid-June. Is Chariots merely hitching a ride on the London 2012 bandwagon? Is it a winner, theatrically?

Designer Miriam Buether has transformed Hall's north London theatre into a mini athletics stadium. There's barely room to swing a cat on the central, circular stage. Nonetheless, the switch from film to live flesh-and-blood is mildly thrilling when Hall's limber actors – including James McArdle as Abrahams and Jack Lowden as his Scottish rival – race round tracks that loop through the stalls. The floor vibrates and you feel the wind in your hair as they pound past – accompanied by bursts of the Vangelis theme tune.

Even so, it's impossible to go hell for leather here, since even a 100m dash is rife with hairpin bends. Scott Ambler's choreography could have been more electrifying if it had been more stylised and inventive.

As for the storyline, Hall commendably makes choppy scenes fluid, overlapping them like a relay race, but some character developments seem rushed in Mike Bartlett's adaptation of Colin Welland's screenplay. And the Cambridge scenes of chaps in boaters and blazers, chorusing Gilbert and Sullivan ditties, is cloying.

It's a slow burn, but what eventually emerges as the really engaging battle of wills is that of Abrahams and Liddell versus the British Establishment – ironic, as they each strive to shine for king and country. Abrahams fights against snobbish anti-Semitism, arguing that his new professionalism is the future and hiring a foreign coach (a beady-eyed Nicholas Woodeson) whom his seniors revile. Meanwhile Liddell's religious strictures are portrayed with striking sympathy. Refusing to compete on the Sabbath, he insists his Christian lore is above the state, the latter being embodied by a caddish Prince of Wales threatening a smear campaign.

There are some fine performances here, including the quietly dignified Lowden, Natasha Broomfield as his devout sister, and the magnetic McArdle who'll surely go far.

The fast movers in Children's Children are of the sexually unsettling variety. In Matthew Dunster's dark new domestic drama, Michael (Darrell D'Silva) and Gordon (Trevor Fox) are best mates, both of earthy northern stock, who've known each other since drama school.

Michael has become a hugely popular TV presenter, earning big money for trash, though he and his new wife, Louisa (Beth Cordingly), try to do good work too, for charities. Gordon's acting career has hit rock bottom. When he begs his friend to bail him out, saying he can't support his family, D'Silva's Michael is almost gallingly munificent. Other skeletons lurk in the closet, too, threatening a history of sleaze and deceit.

This is, in some respects, an old-fashioned play along Shavian lines. There's a nod to Major Barbara, as Gordon's daughter Effie (Emily Berrington) starts out as a censorious teen, upbraiding her parents' compromising work in commercials. She worships her boyfriend Castro (John MacMillan), a documentary-maker on a mission to expose polluting oil companies. Effie then sets up a fashion label that uses a developing world sweatshop. As for Castro, he tries to seduce Louisa while dissing multinationals.

The long speeches about moral choices aren't convincingly integrated and the multiplying nasty twists towards the end feel forced. Nonetheless, Fox's quiet schadenfreude is chilling, the eruptions of fury are savage, and D'Silva is outstanding, seeming to crumple and age before your eyes.

A certain lack of friskiness is afflicting the well-to-do clients of Dr Givings in Sarah Ruhl's In the Next Room aka The Vibrator Play, set in a 19th-century New York spa town. Paul Hickey's po-faced Dr Givings –keener on Edison than Freud's talking cure – has acquired a new electrical gadget for treating hysterics. It looks a bit like a bronze hairdryer crossed with an electric toothbrush.

An unhappily married lady (elegant Flora Montgomery) swiftly perks up, returning for frequent treatments, and Givings has an alternative version that does one gentleman client (Edward Bennett) a power of good too.

Laurence Boswell's production verges, at points, on to Carry On territory, presumably to get the urge to titter out of the audience's system. But when Givings's patients cross paths with his own frustrated wife (Katie Lightfoot) and her new, black wet-nurse (Rakie Ayola), whose own child has died, this chamber play grows into a poignant group portrait. Complicated networks of ardour and tenderness develop, traversing sexual and racial boundaries, and heartbreakingly extending to failed mothering.

'Chariots of Fire': (020-7722 9301) to 16 Jun, then at the Gielgud (0844 482 5130) from 22 Jun. 'Children's Children' (020-7359 4404) to 30 Jun. 'In The Next Room': (01225-448844) to 9 Jun

Posh is back. Laura Wade's dark drama about upper-class youths – inspired by David Cameron's Oxford drinking society, the Bullingdon Club – transfers to the Duke of York's Theatre, London (to 4 Aug). Moon on a Rainbow Shawl, Errol John's tragicomic Trinidadian drama about aspirant post-war shanty-town neighbours is beautifully acted at the NT Cottesloe, London (to 9 Jun).