Even the clock moves at double time. A show set in a series of barber’s shops sounds like a potentially sedentary affair but Bijan Sheibani’s vibrant production – which transfers to the Roundhouse after two sell-out runs at the National and a whirlwind world tour – never stops moving. We roam across shops, shacks and stalls in London and throughout Africa and barely pause for breath. Rae Smith’s makeshift set is on wheels, the barber’s chairs are on wheels, possibly even the actors are on wheels. Inua Ellams’ beautifully observed work is a pulsing and poetic delight; a sweeping snapshot of life as an African man as a dizzying host of customers take a seat, relax and let us into their lives.

Ellams spent six weeks in Africa researching his play, whittling 60 hours of recordings down into this two-hour show. Sometimes the script is almost too rich – there’s so much information to take in – but it’s an undeniably beautiful thing, packed with authentic dialogue and stunning flashes of insight.

Through the chair … Emmanuel Ighodaro and Demmy Ladipo. Photograph: Tristram Kenton/The Guardian

There’s passionate political and personal debate as the men discuss Mugabe, Mandela, fallen leaders and absent fathers. Perhaps the most surprising aspect is just how tender this all-male play feels. Sure, there’s posturing and showboating, especially when Demmy Ladipo’s “bad boy” is showing off to the lads. But there are so many gentle moments in here too: a hard-up old man is given a free haircut; a barber offers a young dad some beautiful advice (“Listen to your child – he will teach you the right language”); and an anxious young actor finds a place to relax and confess his fears.

It’s not just about the dialogue, either. There are the music and movement, overseen by Aline David, which infuse the scene-changes with energy and purpose. There are also the collective sighs, groans and cheers, as the men talk, listen and, of course, watch football. Best of all are the grunts of delight, as each man is shown his new haircut in the mirror. The customers smile and whoop at their reflections, happy – in this safe environment – with the men they see.

• At the Roundhouse, London, until 24 August.