ON 1 NOVEMBER 2011, the Dean of St Paul's, the Rt Revd Graeme Knowles, resigned; Temple, by Steve Waters, is a play that suggests sympathetically why that happened.

It clearly takes place in the context of certain well-documented events concerning the Dean and the cathedral, the City of London, and the Occupy movement. Yet it also claims to be a "fictional account" of these events - not a documentary.

Bishop Knowles was indubitably Dean of St Paul's at the time of the events described in the play; and yet he is not referred to by name, and nor are a couple of the other significant players in this drama. So what is Temple exactly? Apart, that is, from being a stirring, deeply involving piece of theatre?

Set on a single morning in October 2011, Temple turns on the Chapter's decision to reopen St Paul's, a fortnight after it controversially closed its doors because of Occupy London's infamous encampment on its doorstep. The decision to make a U-turn was not an easy one, of course. In the play, a vote has taken place, after a late night of fraught argument, and this is its aftermath.

From the start, the play's director Howard Davies makes sure the audience is constantly reminded of the protesters' presence - of the song repeatedly rising up from the camp to the window of the Dean's office - even if the protesters themselves remain off stage. Over everything looms the dome of Christopher Wren's magnificent edifice.

Waters sets the action in a single room, the Dean's office, giving it the air of an ecclesiastical farce. As he prepares to celebrate the eucharist, and then host a press conference, this (unnamed) Dean receives visits from an (unnamed) Bishop of London, an (unnamed) Canon Chancellor, and others. The Canon Chancellor breaks rank by showily tweeting his resignation at 10.35 a.m.; the traditionalist verger can imagine finding it difficult only if he then shows up for the lunchtime service: "I'll find it very hard to do the Peace with him."

The Canon Chancellor admits that he also took the chance, when he escaped south from St Paul's, across the river, to drop in on Lambeth Palace, where he was received by an impressive but inscrutable Archbishop of Canterbury: "He said almost nothing, as usual."

The Dean, meanwhile, reproaches himself for sanctioning the closure of the cathedral in the first place, and has to resist the dubious blandishments, including cakes, of the City lawyer who comes calling at this point. She takes an alliance between St Paul's and its business-minded neighbours as a given. Those Occupy troublemakers must be moved on. The Dean reminds her about the ancient right to free speech associated with this spot. She leaves, taking the cakes with her.

As you might expect of a Davies production, Temple is theatrically exemplary. At the right moment, an ambulance is heard, blaring its urgent way past the encampment. As the Dean, Simon Russell Beale is the absolute picture of troubled leadership, unable to sit still, or cross the room without giving the impression that hysteria is trying to disguise itself as serenity.

He and Rebecca Humphries, as the Dean's scatty, drafted-in personal assistant, conspire to create a sense of a relationship rapidly developing under the pressure of a crisis. There is a frisson, too, in that this is a show at the Donmar Warehouse: not exactly in the shadow of St Paul's, it nevertheless feels like the right theatre to be re-staging and re-examining a piece of recent local history which happens to have been of national importance.

Russell Beale is, in fact, never off stage, and Temple would be nothing without his virtuosity - his reduction to tears, his gabbling with clarity (how many actors can do that so well?), his way of conveying the intelligence and mildness of a man for whom the phrase "you are vain" (said of the Canon Giles Fraser figure, a self-appointed "Judas") is the weightiest possible insult. And there is nothing wrong with the supporting cast, either, with Malcolm Sinclair giving the Bishop of London a rather absurd, grand air, and Paul Higgins making the Canon Chancellor a wiry, untrustworthy pseudo-spokesman for Occupy.

There are some odd moments in Waters's script, however, which the production struggles to disguise. The Canon Chancellor, for example, feels compelled to return to the cathedral after his resignation. It is not clear why, exactly, but it conveniently leads to a showdown with the Dean, and the necessary scenes of recrimination and reconciliation. The lawyer is a bland caricature. The PA and the verger are not wholly credible.

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It is also strange that Temple is a play scrupulously based on real events and real people, but it chooses to name one and not the other. Occupy London is Occupy London, down to the impossibility of negotiating with such an amorphous organisation. Is Sinclair's Bishop of London Richard Chartres, though? Is it of Canon Fraser or some "fictional" stand-in that he wryly remarks, "Canon Chancellor, you seem to be trending again"? (The Dean who is and is not Bishop Knowles can only bleat impotently "Another tweet!" as some irritating piece of news is announced in the modern style.)

This is a "fictional account" that, for the most part, cleaves closely to fact, in terms of both events and personalities, and yet slips into conversation some (surely) sensational inventions, such as the Bishop's hint that the Dean ought to consider his position. The overall effect is fascinating, unsettling, and possibly entirely misleading.

Temple is at the Donmar Warehouse, 41 Earlham Street, London WC2, until 25 July. Box office: phone 0844 871 7624.

www.donmarwarehouse.com