A Number, Royal Court, London<br></br>10 Rounds, Tricycle, London<br></br>Modern Dance For Beginners, Soho, London

I'd like to allay any fears. If you saw Billy Elliot, director Stephen Daldry's hit movie about a little Northern lad with a talent for pirouetting, you may imagine A Number – the title of his new main house production at the Royal Court – to be a flamboyant follow-up with, maybe, a chorus line of Sloanes finding spiritual fulfilment in clog dancing. No, no, no. A Number is, in fact, Caryl Churchill's latest intellectually teasing, radically fragmented and dreamlike two-hander.

It's performed by Michael Gambon and Daniel Craig with restrained intensity and sly humour on a virtually bare stage (featuring two chairs and an ashtray). Gambon is the nameless father, sporting a high-status suit yet looking rumpled. Craig, who's similarly craggy but physically taut in T-shirt and jeans, is supposedly his son – with hints of an aggrieved lover about him as well.

The surreal or slightly futuristic twist is that the son has been cloned years back, without his consent, as Gambon tried to improve on his original (dead?) beloved boy. Unsettlingly, neither Gambon's memories nor Craig's identity are reliable. Indeed, Craig exits and rematerialises (in Gambon's mind?) as a rougher, vengeful doppelgänger. Then a third reincarnation seems resolutely happier.

Though Churchill's storytelling was more staggeringly ruptured in her previous play, Far Away, her dialogue is again intriguingly elliptical here, hovering between the weirdly stylised and everyday inarticulate chat. Meanwhile, physically, Daldry makes the domestic face-offs absorbingly still, apart from a few spasmodic/iconic gestures of compassion or sorrow – Gambon touching the younger man's face or falling to his knees. Both writer and director manage to be highly economical with, for example, suicidal despair – simply conveyed by the slow knotting of a silk tie. My cavil is I sense a touch of the emperor's new clothes here. The many passing allusions to the Bible and big topical issues (eugenics, ethics, reparation) can feel superficially intelligent with arguments never fully developed. We waltz with ideas here, but aren't much the wiser as we move on.

You probably shouldn't expect 10 Rounds to be exponentially rewarding. Scripted by Carlo Gébler, this is a new Irish reworking of La Ronde – Arthur Schnitzler's Viennese daisy-chain of sexual encounters running through the class system. La Ronde scandalised Schnitzler's fin de siècle contemporaries and, of course, David Hare's recent adaptation, The Blue Room, caused a stir with Nicole Kidman baring all. So I suppose for those who give a fig about stage nudity, I should note a few fleshy bits hove into view at the Tric. Although, really, Nicolas Kent's production is an odd mix of the coy (lights off for coitus) and rather clumsy attempts to shock (with bodily fluids and paper hankies).

What is actually most startling is the political dimension Gébler introduces, updating the action to Belfast in the late 1990s where a peace agreement has been negotiated but may be ditched. So here the prostitute is a Protestant and her first client, quite specifically, a bomb-making Republican who's soon offering to escort an au pair back to her place – a local judge's home.

You might argue the politics make this a meatier state-of-the-nation play than The Blue Room. Also, with a terrorist subplot, 10 Rounds is a thriller that offers a more explosive ending than Schnitzler's relatively inconsequential vignettes. However, Gébler's dialogue is hit and miss. Nicolas Kent's staging includes several fine performances, not least Stephen Boxer as a government official who lets himself be seduced on the job with a brilliantly subtle blend of primness, genuine desire and Machiavellian canniness. The let-down is Kent's penchant for crude comic gags.

Gébler is, in any case, no match for playwright Sarah Phelps whose outstanding London debut turns out to be another (looser) variation on La Ronde. Set in contemporary England, Modern Dance For Beginners is more searingly intimate than pointedly political. For this piece really explores how sleeping around can lead into or on from one unrequited or hopeless obsession. Instead of always moving forwards, Phelps sometimes cuts back to a lover we're meant to have left behind. She also encourages you to bond – though never feel secure – with the characters, as each troubled couple is played by the same actor and actress. Phelps's mood swings from the ardent to the farcical could grate in a second-rate production, but Justin Salinger and Nicola Walker make such lurches feel thrillingly bold in Jonathan Lloyd's vibrant, sensitive production. Raw explicit talk and personal tenderness are extraordinarily intermeshed: Walker plays dirty and hurt with ferocity and Salinger – switching from laddishness to honest declarations of love – is heart-rending. Highly recommended.

k.bassett@independent.co.uk

'A Number': Royal Court, London SW1 (020 7565 5000), to 16 Nov; '10 Rounds': Tricycle, London NW6 (020 7328 1000), to 19 Oct; 'Modern Dance For Beginners': Soho, London W1 (020 7478 0100), to 19 Oct