After winning public and critical approval last year at the Cottesloe, James Graham’s account of the Labour Government of 1974-79 has been kicked upstairs to the Olivier. Gone is the intimate traverse staging in which the audience sits as if on either side of the House — unless, that is, you get a seat on stage on the swivelling Commons’ benches. But what remains is a gripping and fluidly staged account of the sink-or-swim daily life in a minority government.  Graham has done his homework and used his imagination. With the whips as his heroes, he feeds us political backdrop and parliamentary terminology in a way that’s always dramatic. He has fun with the archetypes of toffee-nosed Tories and abrasive Socialists by making the characters themselves have fun with them: Phil Daniels as the Labour Chief Whip Bob Mellish caricatures himself as a “Cockney bruiser” even as he and his fellow Labourites Reece Dinsdale, Vincent Franklin and Lauren O’Neil caricature their opposite numbers.

So Graham, his director Jeremy Herrin and the designer Rae Smith have found the right level of rollicking theatricality with which to make vivid the often farcical survival tactics as Labour galvanises votes from other parties and from MPs who are rebellious, breast-feeding or seriously ill. There’s a house band that moves from hippie to punk as Wilson gives way to Callaghan; a Bowie production number that kills off some of the Labour MPs; and tasty cameos for a Mace-wielding Michael Heseltine and a raffish Alan Clark among others. This post-Enron mix of showbiz and documentary detail wouldn’t fly like it does if the characters weren’t so well drawn. This is a story from ground level that sidelines the nature of the policies in favour of the process of getting them passed. We always know what’s at stake: survival. It feels urgent, as the fine cast of 16 swap roles with focus and aplomb. And you can only relish the top Tories: Julian Wadham as the wittily unctuous Chief Whip and Charles Edwards as his debonair and decent deputy.

Graham appears to mourn the demise of a parliamentary way both adversarial and collegiate. I’m not sure the themes go much deeper than that. But since This House stays so diverting for almost three hours, I’m not sure they have to. And its appeal will spread even farther on May 16, when it will be beamed to cinemas around the country as part of NT Live.

It’s not often that I sit through a three-hour play wishing it longer. But James Graham’s superb new drama held me and I suspect everyone else in the audience enthralled throughout.It is by turns funny, touching and cliff-hangingly suspenseful. What’s more, despite the usual formal insistence that this is a fictional piece, it is almost all true. The action begins in February 1974 when Edward Heath called a general election with the question “Who Governs?”only to receive a raspberry from the electorate who replied “not you matey”. But nor did they ringingly endorse Labour and neither party commanded an overall majority. Harold Wilson formed a minority Government and eight months later went to the polls again hoping for a decent working majority. He achieved one of just three, yet somehow the Labour Government limped on, with the help of shifting alliances with smaller parties, with James Callaghan later serving as PM until 1979 when Margaret Thatcher came to power.

I can still vividly remember those shabby years of industrial unrest, spiralling inflation and the feeling that Britain was a failing nation. I even stood on a picket line myself during the winter of discontent. Graham however confines his play entirely to the Palace of Westminster and the audience sit watching the traverse staging on the green benches of the House of Commons Chamber. A few famous political incidents are staged, among them Michael Heseltine swinging the mace around and John Stonehouse faking his own death. Most of the action however takes place in the Labour and Conservative whips’ offices where the political dark arts are practised and bolshie dissenters are bullied, blackmailed or bribed into submission. Graham has researched his play with exemplary thoroughness and there is a thrilling tang of authenticity about the piece. This you feel must have been what it was really like.

There is also a good deal of comedy, much of it black. Labour’s precarious position wasn’t helped by the fact that so many of its MPs died in office, and we watch them going down like ninepins, as well as the seriously ill being dragged into the Palace of Westminster to vote.  If you wanted to carp you might complain that the Labour characters are generally presented more sympathetically than the Tories, who tend to come over as sneering toffs, but even that criticism must be qualified. The noblest act in a play brimming with bad faith and back-stabbing on both sides comes from a Tory.

Jeremy Herrin’s production ensures that this wordy and complex piece seethes with dramatic energy. There’s a live band to deliver a couple of highly apposite David Bowie numbers, and Rae Smith’s designs memorably capture the Palace of Westminster. There are cracking performances, too. Special praise must go to (Philip Glenister) as a truculent old bruiser of a whip with a warm heart beating somewhere beneath his tough facade, and Charles Edwards as his suave, sharply suited Tory opposite number who in the grubby world of Westminster suggests a genuine generosity of spirit. When the theatrical prize-giving season begins, I have little doubt that This House will be a strong contender for the best new play of 2012.