"We walk, we walk, we walk," chant the hikers of Black Men Walking in a rhythmic refrain. On the first Saturday of every month, an all-black male walking group strides out onto the Yorkshire Moors. It's a leisurely activity – a chance to be myself for a bit, as one of them puts it – but it's a quietly political one too. "We are actively asserting our right to this land."

Rapper, beatboxer and theatremaker Testament's play, the first of Eclipse Theatre's Revolution Mix programme, is as poetic as it is potent. It lets us into a ritual – one that begins with a urinated libation – and into a particular cultural conversation. As they walk, the men talk – about banalities and families, memories and histories. They carve out a space for themselves, as black men in Britain: "We walk out our identity."

This week, there are three of them. Thomas (Tyrone Huggins) is a gruff sixty-something Yorkshireman, whose physical resilience disguises his mental decline. Matthew (Trevor Laird), an RP GP "as English as a Yorkshire pudding," can't put his phone down and his white wife's texts ping into the walk. The youngest, Tonderai Munyevu's Richard, is around 40; a geeky Ghanaian with a toothsome grin. He's just back from a Star Trek convention.

The image of them makes strides of its own, subverting stubborn stereotypes about black men. As well as sewing black bodies into a rural setting, Testament literally redresses them. Zipped into gillets, waterproof trousers tucked into thick socks, the trio looks ludicrous, humdrum and – yes – undeniably harmless. Kidulthood, this ain't.

Walking itself treads a rich seam, echoing civil rights marches, nomadic tribes and the spread of the African diaspora around the world. Three men of different generations putting one foot in front of another, reaching new ground (or, as Richard repeatedly jokes, boldly going) suggests the progress that black men have made in this country – from the overt racism Thomas endured at football grounds in the 1970s to Matthew's middle-class respectability today. And yet, by tracing a Roman road, they're effectively retracing steps black men have made in Britain for centuries – albeit erased. As Thomas reminds them: "We walked this land before the English."

Progress isn't a straight path, however, and, as a white fog rolls in, pointedly restricting visibility, the three soon lose their bearings and start walking in circles. This is, Testament reminds us, treacherous ground. One wrong step can mean a big fall.

His play, tenderly directed by Dawn Walton on Simon Kenny's sculptural grassy-strip set, manages to hold a range of opposing experiences, opinions and identities without delegitimizing any of them. It's celebratory, but it's critical too, exposing the exclusivity of an all-male black walking group. When the trio bump into Ayeesha (a fervent Dorcas Sebuyange), an aspiring MC practising tai-chi on a hilltop, they're soon taken to task for dwelling on the past and entrenching old myths. By walking, she wonders, are they running away? "What is this? Black Last of the Summer Wine?"

But this is a play that pendulums between drama and poetry, spinning off into rhythmic refrains and beat-poems. Its richness outweighs the clumsiness of its reality, but it's not always convincing. Would such regular hikers make such rookie mistakes, ploughing on against weather warnings without working phones? Probably not, but even if metaphor leads, this is a rewarding journey.

Black Men Walking runs at Manchester Royal Exchange until 3 February, then tours to venues nationwide.