The Habit of Art, NT Lyttelton, London<br/>Cock, Royal Court Upstairs, London<br/>Public Property, Trafalgar Studio 2, London

Alan Bennett&rsquo;s hugely entertaining drama tells us much about Auden and Britten &ndash; and just a little about the playwright

The closer you steer to yourself, in your writing, the better you will be. So says W H Auden. No, let’s be accurate. So says the (real-life) actor Richard Griffiths portraying a rumpled (fictional) thespian named Fitz, who has been cast as the great poet in Caliban’s Day – the biodrama being rehearsed in Alan Bennett’s new play, The Habit of Art.

It sounds fiendishly complex but, in practice, Bennett’s pleated layers of art and reality are ingeniously teasing and entertaining. The Habit of Art presents a play being tried out in a (pretend) fractious National Theatre run-through. And Bennett invites his audience to speculate on how much of this might be viewed as semi-disguised autobiography. His programme notes flag up how some of his characters’ experiences have “chimed” with his own.

The self-referentiality is most obvious in the play’s outer frame.Nicholas Hytner’s hugely enjoyable Lyttelton production perfectly re-creates an NT rehearsal room: strip lights; the production team bunched in one corner on plastic chairs. In the centre is a roughly mocked-up set: the aged Professor Auden’s college rooms at Oxford.

A run-through gets under way, with Griffiths’s shamelessly unbuttoned Auden peeing into the sink, casually welcoming a rent boy (Stephen Wight’s Stuart), and dispensing wise words. Crucially, he addresses his artistic advice – about steering close to yourself – to Alex Jennings’s outwardly prim Benjamin Britten.

Visiting his long-estranged friend and ex-librettist, the composer confesses that he’s worried about coming out (even in coded form) as a gay admirer of boys, via his new operatic adaptation of Death in Venice. “It comes quite close to home,” Britten frets. Bennett himself has, of course, been known for his wary reticence, risking a few revelations about his private life of late.

Let’s deal with the outer frame first. The rehearsal set-up is a delight: closely observed, satirically witty and warm. Frances de la Tour is hilariously laconic as the long-suffering Stage Manager. Griffiths’s Fitz keeps forgetting his lines and criticising the nettled Author (Elliot Levey) about his unflattering portrait. Meanwhile, Adrian Scarborough’s Donald neurotically tries to pad out his bit part as Humphrey Carpenter, the narrating biographer of both Auden and Britten.

Now for the core of the piece. Caliban’s Day presents an insightful portrait of Auden and Britten, per se. What makes Bennett’s script simultaneously intriguing, as semi-disguised autobiography, is the shuffling and overlapping of identities – rather like dreamwork. Aspects of Bennett can be glimpsed in multiple characters: in the Author, the narrator-biographer, even in the rent boy.

The playwright, in his notes, also identifies with Britten, regarding Beyond the Fringe. Bennett has previously confessed to feeling overawed by the articulacy of his old friend and fellow Fringer, Jonathan Miller. Strikingly echoing that, he has Britten tell Auden: “I was baffled by the torrent of words ... drown[ing] in your wake.” That said, Auden could equally represent Bennett’s own less repressed side: the voice that tells him to risk exposure. (There were, remember, two Alan Bennetts on stage in The Lady in the Van.)

Admittedly, the mock experimental interludes, in rhyming couplets, wear thin. And Bennett's coda tilts towards sentimentality. All in all, though, this is a great late play, outshining The History Boys. It is an irresistibly droll and critical rumination on artistic principles, the craft of biography, public reputations and private lives, competitiveness and self-censorship.

By way of my own coda, I should probably disclose that I am writing Jonathan Miller's biography (work in progress). However, the last thing this play needs is another character stepping into the frame.

At the Royal Court, Cock by Mike Bartlett is another new play about a gay man coming out. This, however, is a tightly focused chamber piece, electrifyingly played out in a circle, under burning lights. It's as if Ben Whishaw's two-timing John were a specimen under a microscope. This is a verbal wrestling ring. The jump-cuts in John's quarrels with his bruised lover, Andrew Scott's superb M, are like rounds in a fight, punctuated by a bell. Katherine Parkinson's quietly determined W then joins the fray.

The intimacy is scorching. Bartlett's dialogue is painfully funny and intense, alive to the concatenation of petty and devastating comments in domestic showdowns. Cock is a coming-out play with a 21st-century, ambisexual twist. What John finds hard to confess is that he fancies a woman. This is a small but perfectly formed classic.

Finally, Public Property, by newcomer Sam Peter Jackson, is a dark Machiavellian comedy for the noughties: a damning portrait (by an ex-employee) of the PR industry at its most conniving. Nigel Harman's Larry is a slick publicist whose star client, Robert Daws' Geoffrey, is an eminent TV presenter embroiled in a scandal. Crashing through Larry's front door, the paparazzi on his tail, he's been caught in a lay-by in flagrante with an adolescent lad. Steven Webb's shorn-headed Jamie is in tow, visibly shaken.

Jackson's writing needs more time to mature. Several plot developments lack credibility. Nevertheless, staged by Hanna Berrigan, this three-hander has some sharp twists and comic flair. Moreover, Webb is thrillingly mercurial: hilariously naive with a glimmer of cunning. So, plenty of rising talent. Uncannily topical too, after the David Letterman exposé, unless that was all a PR stunt managed by Sam Peter Jackson.

'The Habit of Art' (020-7452 3000) to 24 Jan; 'Cock' (020-7565 5000) to 19 Dec; 'Public Property' (0870 060 6632) to 5 Dec