IF The Culture: A Farce In Two Acts at Hull Truck Theatre in January and February was the first chance in these parts to see why James Graham is all the rage among Britain's rising playwrights, This House is a far better example of why he stands out.

The Culture, an end-of-term report on Hull's year in the spotlight as the 2017 UK City of Culture, was ultimately restricted by its requirement to play to the rules of farce, when the shrewd Graham's greater comedic strength is satire, backed by a forensic understanding of the minutiae of his chosen subject matter.

Last year, Graham had not one, but two plays opening in the West End in quick succession; Ink, the one about Robert Murdoch buying The Sun, and Labour Of Love, the one about 25 years of the Labour Party. Quiz, his account of the Coughing Major story from Who Wants To Be A Millionaire, transfers to the Noel Coward Theatre from March 31.

London, London, and more London. Here in Yorkshire, where he sharpened his tools as a student at the University of Hull, Graham's 2012 debut This House is essential viewing in a Headlong/National Theatre/Chichester Festival Theatre production that captures why the world of politics is so ripe for the stage, be it Shakespeare's Julius Caesar or one of David Hare's verbatim works.

For This House, Graham heads back to 1974, the year of two General Elections, but it is the whips who have the whip hand in this drama. A hung parliament is clogging up the wheels of Westminster, and we start with the stuffed-shirt Tory whips in their smart suits, smart manners and smarting asides holding sway.

The Labour whips, by comparison, have loud suits, kipper ties, frank ways. It was a time of a more obvious political divide between the two main parties by comparison with the homogenised codes of today, and, let's be honest, we miss it.

What works so well here is that we see politics and politicians through the eyes of those who manoeuvre the gaggle of MPs into the all-important voting lobby, battling for control with tactics that bend and even break the rules. As with Armando Iannucci (The Thick of It etc), Antony Jay and Jonathan Lynn (Yes, Minister) and Andrew Davies (House Of Cards), this lends itself wonderfully to both satire and yet not a little pathos too, as Big Ben counts down to 1979 and Jim Callaghan's demise.

Graham spoke in one interview of his belief in his plays seeking to achieve a balance between "where you can speak truth to power" – in other words his authorial voice – and "where power feels comfortable to come and engage in the conversation", and this is exactly what he achieves in This House. Warts and all humanity. Add a huge and hugely impressive cast and superb direction by Jeremy Herrin and Jonathan O'Boyle and This House should get your vote.

This House, Headlong/National Theatre/Chichester Festival Theatre, West Yorkshire Playhouse, Leeds, until Saturday. Box office: 0113 213 7700 or at wyp.org.uk