On the first Saturday of the month, at 9.30am sharp, the men meet just outside Sheffield and head for the Peak District. “By the time we’ve finished,” says 57-year-old Rob, “we haven’t got any stress because we’ve walked and talked it away. That’s one of the beauties of this group.” The men come from a wide cross-section of the African diaspora in Britain. Thirteen years ago, there was just a handful of them, but that’s swelled to about 30, including the occasional woman. Today, on a cold January morning, I’m joining them on a six-mile route around Stanage Edge, a gritstone escarpment in Hathersage, to find out more about the group and the play they have inspired.

When the Ghanaian journalist Maxwell Ayamba co-founded 100 Black Men Walk for Health in 2004, he had one simple aim: get black men walking. “Most black men get to middle age and lead this kind of sedentary life,” says Ayamba. “We are susceptible to all kinds of diseases like diabetes, high blood pressure, vitamin D deficiency.” Research suggests African-Caribbean men are also more likely to experience mental illness.

Ayamba believes exercise and the outdoors can help. Along the way, says Rob, “we have some great conversations about partners, relationships, politics, families, fatherhood and what it is that we need to put in place to protect our children as they’re growing older”. Donald, a geography teacher, says that what he’d most like to gain from the group is “for the next generation of black people to feel confident to be out and about in the countryside in Britain, in a way we perhaps weren’t when we were their age”.

It’s easy for people of my generation to forget just how far the UK has come. In the days of “No blacks, no dogs”, such a group of men walking through the countryside may well have aroused suspicion. A resident of Sheffield for over two decades, Ayamba moves quickly and talks fast. He reminds me of the Ghanaian men in my own family and even crosses his ankles underneath his chair in a particular way, something I’ve spotted in Ghanaian men, from award-winning artists to UN secretary generals. Derek – the oldest in the group – tells me in a lilting Jamaican accent how walking coincided with him finding Christianity. Father-of-two Rob, an amateur boxing coach and bodybuilder, says he loves “just being out of the city. You’ve not got all those fumes. The more I come, the more I feel disappointed I didn’t come years ago.”

Together, the group have scaled Ben Nevis, appeared with Griff Rhys Jones on his BBC1 series Mountain and been recognised in a play, Black Men Walking, which is on at the Royal Exchange, Manchester. Today we are joined by the actors and creative team and an assortment of media people. Ayamba is decidedly nonplussed by all this attention, though. He just wants the walk to start on time.

Black Men Walking was written by the rapper Testament, AKA Andy Brooks, who smiles as he recounts how Eclipse theatre company approached him. “They said, ‘We’d like you to write something about this black men’s walking group in Sheffield – and also tie together over 500 years of black British history.’” Testament had been watching the BBC2 documentary Black and British: A Forgotten History, as well as researching, among others, Septimius Severus, the first black Roman Emperor, and Pablo Fanque, a black circus owner from the 1800s. “I said to them, ‘Can we have a chat over a cup of tea?’”

The son of a Ghanaian woman and “a white dude from Tooting”, Testament grew up in London and Zimbabwe and now lives outside Huddersfield. The thirtysomething father-of-three is, in many ways, representative of modern Britain, moving between race and class boundaries that would have once seemed impenetrable. Since he first came on a walk with the group as research, Testament has come to know the land well, and he makes me want to know it, too. Although, perhaps, some version of me already does. As he says: “Black people have walked these white roads before.”

The more we walk, the more I wonder why the idea of black people hill-walking seemed so strange to me. So many immigrants from Africa and the Caribbean come from rural areas and movement – or more specifically, displacement – goes hand in hand with being part of the African diaspora. Black people on foot have featured in many significant moments in history, from the death walks through West Africa to reach slave ships, to the American civil rights marches in the 1960s. When I think of my family, and of the first and second-generation immigrants I grew up with, I think of them on the move, never still, working second, third and fourth jobs. Perhaps that’s why hill-walking felt so at odds with my blackness at first: this is walking without purpose. Going up then down, arriving in the same spot you left.

Or maybe there is a purpose, maybe there is something about finding yourself in the peaks, or finding the people who have come before you – the black and non-black people who built the country you continually try to claim as also being yours. Walking is a reclamation. Of moving slowly enough to say this is a land you can take your time with; these peaks are safe, I won’t need to run.

So what happens in the play? “Three men are part of a walking group,” says Testament. “On a day when the walk should have been called off because of the weather, they decide to get out as each of them is facing some kind of crisis. As they walk the Lancashire landscape, they – and we as an audience – also encounter the people whose footsteps they’re walking in. Black Yorkshire ancestors.”

Black Men Walking, Testament says, is “a celebration of blackness, of Britishness, and the fighting spirit that Yorkshire has”. I see this on the walk as the men stomp through the Peak District with the matter-of-fact attitude of people who do what they say they will, and always find something positive to say, even when speaking about thorny issues such as race and class.

Dawn Walton started Eclipse in Sheffield after moving there from the south. “We’re a northern company,” she says, “a Yorkshire company, and I’m very proud. We’re black and Yorkshire, y’know what I mean?” Founded in 2010, Eclipse is the foremost black-led touring company in the UK. Three years ago, it launched Revolution Mix, a “movement” that aims to tell stories of black British history. “Every time a black artist is in a costume drama,” says Walton, “people kick off. I don’t know why. Like many of us, I’m very aware of the history – the erasure, actually – of black British people. Researching the last 500 years, it’s a pretty rich scene. And guess what – no one’s told those stories. So that’s my playing field.”

Walton heard about the group from its co-founder, Mark Hutchinson, and was told it was “a safe space for black men”. Curious, she asked to join them. “We were walking in a straight line, and when they said it was a Roman road, my head kind of twitched. I was looking at my feet, concentrating on walking, and I suddenly saw sandals next to me. Septimius Severus, our black Roman Emperor. That’s where the idea came from.”Developing the show has not been without its challenges, the first being the most obvious: how to stage a play about walking, in multiple theatres around the UK, with limited space? Walton laughs. “I did think about treadmills, but no, the actors are using mime techniques.” They are actually working with a clown called Steve Medlin. “We’ve had actors learning three languages: the words they’re speaking, the language of the movement, and the musical elements.”When the walk is over and we are all nursing cups of tea, Bernie, a friendly woman in her 40s, comes over to chat and talks about how excited she is that the walkers are heading for the stage. “Break a leg,” she shouts as she leaves, then pauses. “That sounds like a really bad thing to say when you’re out walking, doesn’t it?”

• Black Men Walking is at the Royal Exchange, Manchester, until 3 February then touring.