In what used to be a warehouse in Leeds, two men are waiting for something – anything – to happen. One rummages in his pockets. The other sucks morosely on a carrot. "The essential doesn't change," decides the first. "Nothing to be done," says the second.

Waiting for Godot might be theatre's most famous representation of a world where nothing changes (twice), but in one major respect this new production is different: the actors, Jeffery Kissoon and Patrick Robinson, are black, as are their fellow cast members. This is the first time Godot has been performed in Britain with an all-black cast.

The production is the brainchild of Patricia Cumper, outgoing artistic director of black-led theatre company Talawa. Cumper was looking for a way to mark the troupe's 25th anniversary, with the help of the West Yorkshire Playhouse. She cackles: "Everyone said, 'Oh, that'd be interesting.'" Ian Brown, who directs, nods. "You need a good reason to do Godot, and I immediately thought this would be it."

Of all the things the play has been interpreted as – a howl of existential angst, a rueful tribute to music hall, quite deliberately about nothing at all – how it relates to race remains an intriguing, and controversial, question. In 1964, it was staged in the American deep south in support of civil rights ("There are those," reported the New York Times, "who want to look at the play and see something beyond Mississippi"). In a black-only South African version in 1976, it became a thinly veiled attack on apartheid; more recently, an African-American company performed Godot in post-Katrina New Orleans, where this story about homeless men waiting on some kind of deliverance acquired a jagged political edge.

Cumper sensed the play could connect with black British experience – not simply as protest theatre, but as an examination of identity. "There are references to being beaten, slavery," she says. "But more subtle things, too: power relationships between the characters, friendships, even the language. I grew up in the Caribbean, and there are many turns of phrase [in the play] that seem familiar."

Although Brown and Cumper insist they're not aiming to evoke a specific time or place – the script is calculatedly vague – things have crept in. Kissoon and Robinson give Beckett's text a subtly African-Caribbean flavour ("digging into our own ethnicity" is how Robinson puts it), making Vladimir and Estragon seem less like tramps or clowns, and more like men in unfamiliar surroundings, perhaps waiting for a new life to begin. "There's Windrush somewhere in the background," reflects Cumper, referring to the ship that brought West Indian migrants to Britain in 1948. "They arrived with these expectations – they could have gone to Paris, they could have gone somewhere else, but they ended up here."

All of which suits Beckett, an Irish writer who moved to France, sojourned in England and developed a style that seems to come from everywhere and nowhere (he wrote Godot first in French, then translated it into English). The play's very open-endedness makes it resonate, Brown suggests; sometimes it feels universal, sometimes eerily prescient. "We've lost our rights?" asks Estragon. "We got rid of them," replies Vladimir. Says Brown: "You don't have any backstory, or sense of who they are. And it doesn't contain the things you expect from a play. But actually, it's full of action, and there is a kind of narrative."

Godot is a good fit for Talawa, a company that showcases the talents of black theatre-makers, not just by commissioning new work from the likes of Bola Agbaje, Roy Williams and Kwame Kwei-Armah, but by staging classic plays that, despite the rise of colour-blind casting, black actors are still rarely asked to perform. British theatre has come a long way, but not far enough, argues Cumper: roles are more limited (just yesterday David Harewood criticised the lack of "authoritative, strong black characters" on British TV), and producers are still unwilling to stage plays by black writers that don't conform to stereotypes of gangland violence or urban poverty. Also, by its nature, colour-blind casting doesn't allow actors to bring their heritage to bear. "There are issues we need to address," she says. "Many things that need to be talked about."

Including Godot? Brown nods: "I don't want people to leave the theatre saying, 'Oh, how lovely – it must have been groundbreaking in its time.' I want it to feel fresh-minted." Cumper smiles. "It's the same play," she says. "The rhythm's still there – but the music's slightly different."