Arguments about Europe, sovereignty, Britain’s place in the world – they’ve all happened before, says Kieran Hodgson. The 2016 referendum was just a cover version. In his new show, ’75, the two-time Edinburgh comedy award nominee traces the roots of our current Brexit malaise back to the 60s and 70s. Few comedy shows since Mike Yarwood’s heyday have leaned so heavily on impersonations of Barbara Castle, Roy Jenkins and Ted Heath. But if Hodgson’s latest is research-heavy – a quality he cheerfully sends up – it’s never fusty. As he did with his unforgettable cycling show Lance and its classical music follow-up, Maestro, Hodgson has created a set that’s enlightening, heartfelt and jam-packed with funny.

There are contrivances at play, more obviously so than in those earlier successes. Hodgson begins with a precis of his loving relationship with his mum, culminating on 23 June 2016, when she votes to leave the EU and he calls her a “racist Merlot-sozzled old witch”. Traumatised by this rift – and shocked that Cameron’s referendum has cleaved families and friends into hostile camps – Hodgson repairs to the library, where a kindly German guides him through the books he must read to fathom our relationship with modern mainland Europe.

It feels a mite effortful this, as Hodgson seeks to recast his bookishness as high drama. But that’s easily forgotten as he plunges us into historical debates about Britain’s postwar decline and the emergence of the common market. This could be thin gruel, comedically speaking – as Hodgson acknowledges in numerous arch asides. But in his hands it’s a near-constant hoot, as the Beatles advise Harold Macmillan on his foreign policy, a Labour party civil war is recast as West Side Story, and Charles de Gaulle airport (boom boom) is reincarnated as RuPaul.

Huddersfield hero … Harold Wilson in 1976. Photograph: ITV/Rex/Shutterstock

Hodgson’s considerable skills as a vocal caricaturist are part of the pleasure here; so too the frequency and quality of the jokes, from those mocking our host’s nerdiness (witness the song he wrote to memorise every English county town) to those about Harold Wilson’s obsession with sandwiches. But it’s not just about the laughs, it’s about the learning. Along the way, Hodgson’s research reveals that the link between Europhilia and elitism has deep roots, that sovereignty-anxiety isn’t unique to rightwing maniacs – and that there’s much to be said for his fellow Huddersfield man Wilson’s brand of canny compromise. If not a common market, we at least need common ground – and to be able to love those with whom we disagree.

Hodgson strains to make these discoveries emotionally significant, as – closing in on a slightly weak denouement – he seeks rapprochement with mum. More affecting, perhaps, is Jenkins’ speech about decriminalising homosexuality (an example of leading rather than following public opinion from which later politicians might learn, Hodgson implies), and the episode he dramatises in which awkward, kindly Ted Heath is commissioned to execute a German prisoner-of-war. Here, the laughs momentarily subside, as the impulse behind the EU’s creation is laid bare.

Of course, Hodgson is soon undercutting this with rueful gags about his hero Heath’s feet of clay. But that sonorous moment echoes throughout this terrific show, which marshals a cast of postwar political titans to show we can at least laugh at our recent history of Britain-never-quite-in-Europe, even if we seem endlessly doomed to repeat it.