I Am Thomas, Royal Lyceum Theatre, Edinburgh

"Thomas Aikenhead – who the fuck are you?" So goes the refrain to the opening number of I Am Thomas, a boisterous co-production between London’s Told by an Idiot, and the National Theatre of Scotland and Edinburgh’s Lyceum Theatre north of the border. It’s a good question, one that acknowledges few in the audience will be familiar with the show’s central figure. And also one that raises the issue of why we should even care about some guy we’ve never heard of.

So who is the Thomas of the show’s title? He’s the last person to be executed for blasphemy in Britain, in Edinburgh in 1696, a 20-year-old medical student at Edinburgh University shopped by acquaintances for a few ill-considered remarks calling into question Christ’s miracles and the holiness of the Trinity, and who came up against the particularly malicious Lord Advocate James Stewart (with a few scores to settle himself), who insisted Aikenhead should hang for his crime.

It features the first non-ironic mirrorball I've seen on stage for a while

Told by an Idiot’s self-described "brutal comedy with songs" tells Aikenhead’s story through song and speech, his role passed back and forth between actors in the eight-strong cast and indicated with a literal but chilling "I Am Thomas" sign on their T-shirts or round their necks (pictured below). The show has already toured to Liverpool, Salisbury and Salford, and continues to Inverness before a run at Wilton’s Music Hall in London. But I Am Thomas has particular resonance in the city where its shameful story takes place, its locations of blasphemous remarks, trial and execution only a short distance from the Lyceum Theatre itself.

It’s an exuberant and sometimes uncomfortable mix of elements, though, one that reimagines Aikenhead’s story in a kind of retro 1970s-meets-1690s setting, and whose plentiful songs – good numbers, too – sometimes actually muddy rather than clarify the storyline. In devising the production, director Paul Hunter and the cast have thrown so much at it that inevitably only certain things will stick.

There’s the company’s trademark irreverent humour, and pop culture references from Life of Brian through to Jacques Cousteau. There’s even a recurring Match of the Day-style commentary where football pundits analyse Thomas’s increasingly desperate predicament in clichés and agonisingly mixed metaphors – and although it jars deliciously with the sombre events around it, the joke quickly wears pretty thin. There’s designer Laura Hopkins’s deliberately makeshift, old-fashioned set, like a Fringe show writ large with anachronistic tumbling backcloths. And there are the songs, sometimes channelling Brecht and Weill, other times sounding more like Sondheim, specially written by Edinburgh-based musician Iain Johnstone with knowing lyrics by Simon Armitage.

They’re delivered by a cast in remarkably fine voice, particularly the beautiful, African-inspired vocal improvisations from John Pfumojena. They pit pitch-black humour against genuine pathos, and a kind of sarcastic, arch knowingness against disarming sentimentality, particularly in the show’s tragic final scene, which must feature the first non-ironic mirrorball seen on stage in a while.

It’s exuberance bordering on excess. I Am Thomas’s seemingly sole example of restraint, however, is in its signposting of modern parallels. The closest it comes is a single T-shirt in the show’s final scene that replaces the usual "I Am Thomas" text with "Je suis Thomas", a clear nod to the "Je suis Charlie" slogan. By the end, we’re in no doubt as to who the fuck Thomas is, but the show needs a bit more emphasis on its parallels with contemporary events to make us truly care about him.

• I Am Thomas continues at Edinburgh’s Lyceum Theatre until 9 April, before travelling to the Eden Court Theatre, Inverness (12-16 April) and Wilton's Music Hall, London (20-30 April)