Thomas Aikenhead was hanged at the age of 20, the last person in Britain to be executed for blasphemy. Raised as a Christian, in an era of religious orthodoxy, the Scottish student insisted on man's duty to the truth all the way to his death, in 1697, under the prosecution of the Lord Advocate James Stewart.

In a very real sense, we are all Thomas Aikenhead now. His rational scepticism has become the norm – a point well made in Told By An Idiot's scrappy comic musical. Each actor takes their turn to step into his shoes, the words ‘I Am Thomas' emblazoned on their costume to run through the stages of his life, from his education to his trial. While his establishment prosecutors wear the lace cuffs and powdered wigs of the period – a style passed down from the king himself, Charles II – Aikenhead's in modern dress to stress the progressiveness of his ideas.

I've a real soft spot for Told By An Idiot. Paul Hunter and Hayley Carmichael put silliness to serious purposes, using dumb comedy to smuggle in dangerous and difficult ideas. Who else could address international terrorism through the medium of Are You Being Served? or tease out the sexual politics of TISWAS.

Here, they use a form of lowly, popular theatre to reclaim Aikenhead as a people's hero. I Am Thomas marries the political poor theatre of Brecht and Weill with the broad comedy of British music hall – a natural fit for a rejuvenated Wilton's Music Hall. Hunter's production raids dressing up boxes and joke shops for the sake of cheap gags, revelling in the shonkiness of village halls and school nativities, while Iain Johnstone's songs – though they can stall for time – shuffle from poignant lyricism to raucous sing-a-longs. Sometimes, though, the scrappiness swallows Simon Armitage's delicate lyrics whole, and, despite the eager energy of its game cast, there's a sketchiness to its Match of the Day spoofs that means scruff wins out over nuance.

For all the brilliance of its conception, though, I Am Thomas hasn't the intellectual daring of Told By An Idiot's best. At heart, it's a straightforward celebration of independent thought, those free radicals that dare to swim against the tide of their times. It's laced with similar icons: David Bowie T-shirts and safety-pinned punks. Even Albert Einstein drops in for a dream sequence.

At the same time, it questions who we chose to honour as our national heroes: those that changed the world or those that kept it in check? Aikenhead's story is framed by a debate over a public statue – timely, in the wake of the ‘Rhodes Must Fall' movement, pushing against the celebration of colonialists – and in putting Aikenhead on a pedestal, it attempts to right the wrongs of history. It's less successful in thinking about the present: the Aikenheads of today. That its shot through with shards of African music – John Pfumojena, stalking the stage in silence, unleashes the most extraordinary voice – looks uncomfortably close to tokenism; an uninterrogated nod to unheard voices the world over.

I Am Thomas runs at Wilton's Music Hall until 30th April.