There’s a party going on. Damon Albarn is busy improvising on a thumb piano. Sola Akingbola, the drummer from Jamiroquai, is playing a shuffle on a shekere (a large maraca strung with beads). And Cuban dancer Yanet Fuentes is shivering her hips to the rhythm. In the middle of it all sits theatre director Rufus Norris – the man responsible for harnessing this hubbub and putting it on stage.

These are the rehearsals for Feast, a new play tracing the spread of the Yoruba belief system and culture from its home in Nigeria to Cuba, Brazil, the US and UK. Since he began directing in the late 1990s, Norris has sought out difficult projects – among them London Road, a jagged musical dealing with the aftermath of serial killings in Ipswich; and Dr Dee, Albarn’s first opera, about a 16th-century alchemist. (The two have remained friends, hence Albarn’s open ticket to this rehearsal room in a London warehouse, even though he’s not in this show.)

Feast is no exception. It has five writers, who live in four continents, and a cast of 13. The story covers 300 years of Yoruba experience, taking in slavery, liberation, family and social politics. But Feast isn’t a history lesson, says Norris, and if it’s going to feel authentic to the Yoruba belief system – in which everything from a table to a sheet of plastic has its own spirit – “you can’t just have a load of blah-blah on stage”. Which is one reason why, right now, he’s gently arguing with his choreographer, George Cespedes, about the actors’ intricate dance moves. Norris thinks they will liven up the staging; Cespedes, who is used to having more rehearsal before curtain-up, is getting worried about the time.

Feast was dreamed up by Elyse Dodgson, who runs the international department at London’s Royal Court, which is co-producing the show with the Young Vic. In the mid-2000s, Dodgson happened to be working simultaneously with playwrights in Nigeria and Latin America, and was struck by how the orishas, or spirits, of Yoruba belief had travelled across the Atlantic with the men and women who were transported as slaves, and fused with Catholicism to form the basis of local religions: santeria in Cuba, candomblé in Brazil. “It’s such an amazing story of survival,” says Dodgson – the trouble was how to tell it. It took two years of workshops, involving as many as 10 playwrights, to reach the form Feast is in now. Those workshops, writer Gbolahan Obisesan admits, were a tussle, as he and his fellow writers struggled to “agree on something that links all of us together”.

Norris insisted from the beginning that he didn’t want the show to feel like a string of vignettes, so Feast coalesced around four figures drawn from Yoruba cosmology: Yemoja, the mother goddess; Oshun, goddess of love; Oya, the spirit of change; and Eshu, the trickster, who causes chaos wherever he goes. These are reincarnated across the show, taking the form of sisters separated by slave traders, civil-rights protesters in 1960s America, and athletes in modern London vociferously debating whether black people should have white lovers or white bosses. Each of the five writers – American Tanya Barfield, Cuban Yunior García Aguilera, Nigerian Rotimi Babatunde, Brazilian Marcos Barbosa, and Obisesan, who moved to the UK from Nigeria in 1990, when he was nine – is responsible for the segments set in their own country.

Clearly this hasn’t been the simplest of ways to work (just trying to interview the five writers proves almost impossible). Why not settle on a single voice? Babatunde speaks for all of them when he says: “The dynamics of the story of Nigerian diaspora can only properly be reflected by the changing tones of each section.” Barfield adds that, given the hybrid nature of much Yoruba culture, there was no other way: “It’s rare to have the structure and the theme [of a play] work so much in tandem. The weaving of the stories mirrors the weaving of belief systems.”

Norris suggests a more down-to-earth reason: “There are details in the Cuba scene that nobody who wasn’t from there would come up with. Similarly, nobody can really write the Nigerian scene unless they have a deep understanding of the women there.”

Strikingly, the five writers met only once, in London last spring, but discovered links between them both expected and unforeseen. Babatunde knew the orishas had travelled to Latin America with slavery, but hadn’t realised how openly they are worshipped in Brazil and Cuba. For his part, Aguilera knew that orishas inform a lot of day-to-day Cuban rituals (such as the deliberate spilling of the first drop of rum from a bottle, to appease the spirits), yet it wasn’t until he was in London that he attended his first santeria ceremony.

The writers found connections in their different upbringings, too. “When you step out of the household [in Nigeria],” says Obisesan, “you’re not just a representation of yourself as a human being, you represent the whole family, the house you were brought up in. You represent your ancestors.” That’s something Barfield was surprised to recognise from her Oregon childhood: “Many black Americans have no knowledge of our ancestors whatsoever, yet the belief system of ancestral heritage is fundamental to the black community.” And although she was brought up Christian, the Yoruba belief in pervasive spirits did feel familiar: “The idea of God being everywhere is very much a part of African-American belief.”

This notion of pervasive spirits was key to Norris’s staging of the Wole Soyinka play Death and the King’s Horseman at the National Theatre in 2009: the audience could see that the props and furniture were “alive” because they were given life by puppeteers, but the white colonial characters couldn’t. Norris lived in Nigeria for the first three years of his life, while his father taught in a university there; to him, belief in spirits makes perfect sense. “It’s not romantic. There’s an energy to things, and the people there have a deep understanding of that.” He remembers reading an interview with a Yoruba priest who, at the suggestion that his beliefs were mere superstition, replied along the lines of: “If somebody is blind, you cannot talk to them about sight. You can’t see it; I can. I’ll just have to allow you to remain in ignorance.” Such resilience helps to explain the tenacity of Yoruba culture, he suggests: the way it survived slavery, its permeation into other lands.

For all his belief in Feast, Norris is anxious about putting it on stage. Not only do multi-authored plays tend not to go down well with critics, but this is the latest production from World Stages London, a collaboration between eight London theatres whose work last year – including outdoor community piece Babel, pan-European play Three Kingdoms and Bollywood musical Wah! Wah! Girls – received mixed reviews. “If I’m honest, I’m bracing myself,” says Norris. “But this is a celebration of an amazing culture – you can’t deliver that in a lecture form. And our theatre needs to open up.”

And with that, he goes back to the Latin dancers, the uplifting rhythms, the vibrant story of saints and survivors.