The films, collectively titled Small Axe, will air on BBC One and BBC iPlayer in November.
Wright stars in Mangrove, which tells the story of the trial of a group of nine protesters against police harassment who were of West Indian, African and South Asian heritage. It will open the BFI London Film Festival with the European premiere taking place on 7 October.
Watch the trailer for Small Axe below...
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The trailer appears to show her character taking part in a demonstration.
Boyega, who stars in Red White And Blue, appears in the trailer dressed as a policeman.
The film tells the story of forensic scientist Leroy Logan, who is played by the actor, who wants to do more work outside the laboratory to change what he sees as the racism within the police force.
Boyega responded to the launch of the trailer on Twitter, quoting lyrics from the Bob Marley and the Wailers song from which the show title is derived.
So if you are the big tree, we are the small axe. Ready to cut you down, cut you down.— John Boyega (@JohnBoyega) September 20, 2020
Education, Alex Wheatle and Lovers Rock are the titles of the other films in the series.
In 2014, McQueen became the first Black filmmaker to win the Academy Award for Best Picture with the harrowing historical drama 12 Years A Slave. It also won the Best Film BAFTA and the Golden Globe for Best Motion Picture - Drama.
Watch the trailer for Widows below...
He made his feature film debut in 2008 with Hunger, starring Michael Fassbender as political prisoner Bobby Sands, which he followed in 2011 with Shame, also starring Fassebender.
His last film was 2018’s crime thriller Widows, and Small Axe marks his first foray into television.