Adapt a best-seller and you are already onto a winner. But when it comes to political diaries you'd have thought the rule wouldn't apply – the confessions of a middle-aged, well-off, fairly successful politician aren't particularly glamorous stuff. However, Michael Chaplin's tight adaptation of former Labour MP Chris Mullin's diaries proves that, in the right hands, walk on parts can take centre stage.

One of the shows major feats is that it manages to stay interesting. Director Max Roberts, who directed the National Theatre's acclaimed The Pitman Painters, paces the piece perfectly: it races along without losing time for thoughtfulness. Mullin is clearly thinking his way through an important decade; picking his way through the detritus of a political career to tell this story. The play opens with Labour's landslide victory at the 1997 election, and closes with their defeat in 2010. It is interesting to see such a recent period mapped out from start to finish like this, and the use of news footage (more of this would have been good) helped to give shape to it with political reference points. A grid of screens on the back wall sets the scene, showing the events of 9/11, archived pics of long-reneged handshakes and contemporary caricatures.

Of course the play's energy is largely down to John Hodgkinson's witty, sympathetic and balding portrayal of Mullin. He talks animatedly to the audience about the latest scandal in Westminster and confides in us when weighing up his political prospects or recalling a family day at the beach. Then he lurches back into dialogue and a back-room scene or telephone call circa 1999 is brought brilliantly to life. The tone is always truthful and choppily like a diary. The parochial anecdotes run the risk – you would have thought – of being either twee or dry, but in fact the play is engaging throughout.

Partly what keeps it alive is the authentic mix of personal, domestic and foreign affairs. Mullin wants a traditional Northumbrian walled garden to tend to in his retirement; he also wants some evidence for weapons of mass destruction. When things don't work out in Westminster because he has been too vocal in his criticism and concern, he spends an afternoon murdering the snails and renews his battle with the local Leylandii bushes.

As Hodgkinson drives the thing forward, the rest of the cast snap between characters in illustrating the anecdotes with instantly recognisable impersonations of Brown, Blair and Prescot etc. A glossy Cameron is attracting attention somewhere off-stage, and Tracy Gillman is Chief Whip Hilary Armstrong one minute and Mullin's Orlando Bloom-stricken teenage daughter the next. Meanwhile a sensitively portrayed day-to-day of MP's surgery – a stream of asylum seekers whom Mullin is usually impotent to help – sits alongside the satire.

There is something of The Thick of It about Chaplin's piece, but essentially it is a rather affectionate portrayal of a relic from an age when Labour politicians knew what they stood for. Mullin isn't too good with a pager but, as his genuine dedication to his Sunderland South constituency shows, he is certainly not out of touch. And lines like, “I doubt there is a future for an economy based on shopping” can't help but linger with you.

A Walk on Part: The Fall of New Labour, at Arts TheatreBecky Brewis reviews A Walk On Part at the Arts Theatre.4