While the political anoraks will be checking it for historical accuracy, anyone else settling down to watch Coalition, Channel 4’s dramatisation of the frantic days after the 2010 election, will want to know if it is watchable. It is. It is a very well-spun yarn, told at a rapid pace, with no pointless monologues or didactic pointers that direct you to the author’s message.

There is even character development, something rare in a drama about contemporary politics. Gordon Brown, played by Ian Grieve, is first seen as a man in obtuse denial, thrashing about oafishly in vain hope of securing a coalition deal, until there is a moment of self-awareness that comes upon him in the odd setting of a puddle ridden tunnel under Whitehall. From then, it is a fight to bow out with dignity. Grieve has also played Gordon Brown in Kevin Toolis’s stage play The Confessions of Gordon Brown, but this Gordon Brown and that Gordon Brown are two distinct characters. This is the kinder portrayal.

David Cameron comes over as a man without self-doubt or great depths; a political version of Piers Morgan. While the other lead actors described the trouble they took studying their characters in detail, Mark Dexter told journalists, jokily, that he spent “half a day panicking like hell” then got on with it – which, one suspects, is rather like the real David Cameron’s approach to political crises.

Through most of the action, the centre stage is held by Clegg (Bertie Carvel). The portrait is not flattering. At times, he makes the Lib Dem leader sound like Uncle Bryn from Gavin and Stacey, at other times like Hugh Grant in Four Weddings, not knowing which girl to marry.

I suspect that, behind the scenes, the real-life Nick Clegg was calmer and more decisive, but talking to journalists after a private screening on Monday night, Carvel emphasised he was focused on creating a good drama, not on an accurate impersonation.

Paddy Ashdown is portrayed by Donald Sumpter, one of those actors you have seen in countless dramas without quite registering his name, who plays the ex-leader like an honest retired copper watching the young detective crack the case. “I’m worried about Nick – he’s in a bad place,” he says at one point early in the action. “Sheffield?” ask David Laws (Richard Teverson). “I mean emotionally.”

The other star turn is by Mark Gatiss, playing Peter Mandelson as a sly, battle-scarred courtier clever enough to see that Labour has lost, but loyal and devious enough to play the coalition game until that moment of epiphany in the underground tunnel.

Writer James Graham, has an established reputation for thorough research and it is a great story. Watching it will be excellent preparation for the events that will follow the election in May, when once again the political parties will be wheeler dealing to decide who gets the keys to No 10.