The Little Dog Laughed, Garrick, LondonSix Degrees of Separation, Old Vic, LondonThe Rivals, Southwark, London

A storming Tamsin Greig channels her inner bitch in a snappy US satire on Hollywood, hypocrisy and homophobia

Mitchell is a fictive Hollywood star. Indeed, this pivotal character in the West End's entertaining new American satire, The Little Dog Laughed, is a fabrication in more ways than one because the public persona Mitchell maintains, to safeguard his lucrative popularity, is a tissue of lies.

Penned by the fast-rising writer Douglas Carter Beane, this is a contemporary comedy of manners which lampoons the hypocritically homophobic and image-manipulating movie industry, while secreting a tender gay love story at its heart.

In director Jamie Lloyd's snappily stylised British premiere, Rupert Friend's lean and bronzed Mitchell is in denial about his sexual inclinations. Then he falls for a scruffy rent boy, Harry Lloyd's sweet, tentatively reciprocating Alex, and decides to come out of the closet.

However, Mitchell's agent, Tamsin Greig's ferociously hardnosed Diane, insists he keeps up the pretence. Though non-hetero herself, she is hell-bent on elbowing Alex out of the picture and setting the record "straight" with a paparazzi-placating wedding, involving Alex's photogenic ex-girlfriend, Ellen – that's if she can be bought.

To call The Little Dog Laughed a biting satire would be extravagant but Carter Beane certainly isn't afraid to nip the hand of the entertainment industry that feeds him. Showbiz machinations are an easy and familiar target, the mock-happy ending shallows out any profound sense of loss, and Gemma Arterton's Ellen strains to be as amusing as the others.

Nevertheless, Lloyd and Friend are both droll and touchingly passionate, stripping down to their pants in a frenzy of desire. And Greig is absolutely storming, combining deadpan sardonic digs and flamboyant swish. Vogueing in a black evening dress, she's like a Prada-wearing Wicked Witch of the West Coast, while making out she's everyone's fairy godmother, dispensing dollars and dreams.

Deception and slippery identities slither on, as running themes, in Six Degrees of Separation, John Guare's hit Manhattan drama from the 1990s.

Played by Obi Abili in a major new production at the Old Vic, Paul is a spellbinding impostor. An Afro-American underdog and compulsive fantasist, he has forged a scintillating new identity for himself. You might say he's the Eliza Doolittle of New York hustlers, or a potentially dangerous distant cousin of Billy Liar. Having been picked up on the street by a preppy gay guy, he demands lessons in elocution and social niceties. Soon, pretending to be the Harvard-educated son of Sidney Poitier, he proceeds to charm the socks and wallets off a string of wealthy Upper East Siders, including a suave art dealer called Flan (Anthony Head) and his wife, Ouisa (Lesley Manville).

The trouble is, this revival leaves you feeling slightly cheated yourself, as if there's something tricksy about the play per se. Guare's storytelling keeps changing tack – with flashbacks – in a manner that feels flashy. And the rich socialites' petulant kids, who Paul claims were classmates, are annoyingly sketchy cameos. Frankly, it's not surprising that Flan and Ouisa are wowed by his elaborate hoax when their own offspring are such unconvincing caricatures.

And yet, the play's titular concept – the idea that we're all connected to everyone else via half-a-dozen (or fewer) social links – does cut startlingly through class strata and racial divides. The problem is that, with Ouisa spelling this out more than once – and Manville milking it – Guare starts to seem a pseud, especially when he throws potted theses on Kandinsky and Catcher in the Rye into the dinner-party mix.

That said, the deep marital unhappiness that Manville ultimately reveals, and her final phone conversation with Abili's still shifty but desperately needy Paul are transfixing. Abili is certainly a star player, even if this production, with astounding racial insensitivity, makes him play second fiddle to Manville at the curtain call.

Finally, up-and-coming director Jessica Swale has lined up a notable cast for her fringe production of The Rivals, Sheridan's 18th-century comedy of duelling suitors and confused identities set amid the social whirl of Bath Spa. Swale's ensemble, in low-budget period dress, are pleasingly buoyant, immediately creating gossipy intimacy by winking at the audience during their asides. They also launch into a square dance to the wittily folksified tune of Beyoncé's "Single Ladies (Put a Ring on It)".

Unfortunately, these winning tactics don't enjoy further development. Harry Hadden-Paton cuts a dash as the incognito aristocrat Jack Absolute, but Celia Imrie is on automatic pilot as the pea-brained Mrs Malaprop and Ella Smith (from the West End hit, Fat Pig) is completely wasted as Lydia Languish's bland friend, Julia. Both are outshone by their wanton maid, Jenni Maitland's Lucy, and Christopher Logan as the cowardly bumpkin Bob Acres is a wonderfully etiolated twit in a frock coat.

'The Little Dog Laughed' (0844 412 4662) to 10 Apr; 'Six Degrees of Separation' (0844 871 7628) to 3 Apr; 'The Rivals' (020-7407 0234) to 30 Jan

Next Week:

Kate Bassett finds out what the acclaimed experimental troupe Filter has done with Chekhov's Three Sisters as they strip it bare at the Lyric Hammersmith