John Boyega and Letitia Wright head the cast on Steve McQueen's latest project, an anthology series set within London's West Indian community.
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Alex Jennings and Line of Duty actress Rochenda Sandall will also appear in the series, which will tell five different stories across six episodes.
McQueen said Small Axe would be "local but at the same time global".
He said the drama's "dynamic nature" would enable it "to confront injustice in the face of adversity".
Shooting on the series, to air on BBC One next year, began this week in London.
It is not yet known who Boyega - Finn in the recent Star Wars films - and Wright - Suri in Marvel's Black Panther - will play in the programme.
The British stars - who both studied at London's Identity School of Acting - are also set to co-star in sci-fi romance Hold Back the Stars.
McQueen, whose films include 12 Years A Slave and Widows, said he wanted to "re-live, re-evaluate and investigate the journeys that my parents and the first generation of West Indians went on".
Its title derives from a Jamaican proverb ("If you are the big tree, we are the small axe") which Bob Marley also appropriated for a song on his 1973 album Catch a Fire.
Piers Wenger, controller of BBC Drama, said it was "an honour" to help the Oscar-winning film-maker "tell these important and inspiring stories".
Amazon will co-produce the series, which according to Deadline will centre around a small restaurant in London's Ladbroke Grove area.