Catherine Tate and Timothy West in The Vote
Catherine Tate and Timothy West in The Vote
© Johan Persson

This review appears on Election Day in 2015, the last night of The Vote at the Donmar Warehouse, and the same night as the show is transmitted live from Covent Garden on Channel 4's More4 tributary - over the last 90 minutes before the polls close at 10pm.

Could theatre be more cosily "happening" than that? Or more calculated? But Josie Rourke's production, and James Graham's play - following on from This House at the National and Coalition on Channel 4 - is another hilarious exercise in political anatomisation, only from the bottom up: in a polling booth in the south London constituency of Lambeth where Graham lives.

Lambeth is not a marginal seat but, for the purposes of the play, it is. We the audience cast our votes for fictional candidates on Robert Jones's primary school gym set of mini-chairs, climbing ropes and parquet flooring; then, at 8.30pm precisely, the play begins with the arrival of voters in the temporary domain of Mark Gatiss as the presiding officer and his council worker helpmates, Catherine Tate as Katy and Nina Sosanya as press officer Laura.

With the coming and going of a television soap - EastEnders is referenced both in Gatiss playing the theme tune on the piano and Timothy West (lately in the series) shuffling on as a multiple-voting senescent side-show – threads of plot coalesce around spoilt and fraudulent papers, ingeniously devised, ending in a climactic and criminal disaster.

Tate's Katy enlists her family in the cover-up of matching red and yellow Haribos in the sweet jar (ie the voting booth) with the blue they assume West's Fred Norris has snaffled. Katy's also moved centre stage because she's broken down the school door with an axe as the caretaker's gone missing and the security video's gone viral, resulting in a Swedish film crew arriving on the doorstep to make her a star.

'It wins my vote more easily than anyone in my local constituency'

Some of this plotting remains peripheral, as do the incursions of a post-nuptial lesbian couple (Wanda Opalinska and Pandora Colin) and a warring pair of sleek banking yuppies (Rosalie Craig and Nicholas Burns). But the realism of this deficiency is that you go into a polling station, vote, and leave. That's it.

Judi Dench in The Vote
Judi Dench in The Vote
© Johan Persson

Other characters such as Hadley Fraser's drunk loud mouth, Gerard Horan's Conservative agent and Bill Paterson's SNP school caretaker (celebrating this very day the birth of his grand-daughter, Nicola), kick into the action neatly.

And the black comedy of one person one vote is beautifully elaborated with the arrival of Judi Dench and her daughter, Finty Williams, playing a furious mother and daughter - Judi a retired nurse, Finty an obviously despised (by mum) hospital management employee - who have been mistakenly registered under the same name.

Other incidental treats include the appearances of Olivier-award winning RSC Henry VI Chukwudi Iwuji as the Conservative candidate and Paul Chahidi as an explosive, self-destructing independent obsessed with the borough's one-way traffic system ("One Way? No Way!" is his ticket).

But the play manages, too, to be the tragedy of an idealistic public servant - not a politician, but Gatiss's funny, fruity, humble vote-counter; what a wonderful actor he's become - overwhelmed by flawed behaviour in the democratic process. It's a lovely, detailed performance in a play that has legs beyond the immediate application, and it wins my vote more easily than anyone in my local constituency of Holborn and St Pancras, that's for sure.

The Vote will be broadcast live from the Donmar this evening from 20:25 on More4