Who'd have thought that, in their pensionable years, those former firebrands David Hare and Howard Brenton would turn keepers of England's history.

But it feels that way. At Hampstead Theatre, not long after Hare's The Moderate Soprano reminded us of the idealistic foundation of Glyndebourne, Brenton's Lawrence After Arabia turns the pages of the past to mark T.E. Lawrence's passionate advocacy of the Arabian cause – and make the point that in carving up the Middle East for its own ends, Britain laid the foundations of the region's current problems. And so of its own.

This is a funny old play, traditional in form and not particular radical in content, though it does take on board recent scholarship which suggests that Lawrence and his account of events were even more complicated than we knew. But it is written with a rare and engaging affection for its participants. In the programme essay, Brenton recalls the photograph of Lawrence on the wall of his primary school – a visionary hero whose image has never left him.

We first meet Lawrence when he is in crisis, running away from the celebrity that he has provoked thanks to his part in the successful Arab Revolt against the Ottoman Empire. It is 1922 and he has enlisted in the RAF under the assumed name of John Ross. As news of this begins to percolate, it causes a scandal for the British establishment. "You can't have an officer and a gentlemen cleaning lavatories," harumphs William Chubb's marvellously stiff-upper- lipped Field Marshall Allenby, Lawrence's former commander.

Lawrence (sensitively played by Jack Laskey) is seeking to reinvent himself, and takes refuge in the home of George Bernard Shaw (Jeff Rawle, very funny) and his loving wife Charlotte, who also carries a torch for the younger man. Geraldine James luminously suggests the depth of Charlotte's care for both men, creating a sense of a woman trying to make herself a meaningful life in small acts of kindness.

With the help of a stylish set from Michael Taylor, which breaks apart to evoke the wide open spaces of the desert, and gentle direction from John Dove, what follows is an examination of Lawrence's reasons for despair; a revelation of the deep guilt and self-disgust he feels about his betrayal of the Arab cause because he always knew that the British and French had already carved up their dream kingdom with "straight lines." "I reek of bad faith," he says.

Brenton can't resist underlining this point - "we have no idea as a civilisation; we may even have destroyed ourselves" – and the play occasionally suffers from the Mr Shaw meet Mr Lawrence form of dialogue. "But you founded the London School of Economics," Lawrence tells Charlotte at one point. Yet it's also full of wonderful, zinging lines, and a sharp-eyed observation of the collision between Bohemian values and establishment rules. It's a quiet reminder that recent history matters. I rather loved it.

Lawrence After Arabia runs at Hampstead Theatre until 4 June.