Wright will play The Girl in a cast that also features Likely Lads star Rodney Bewes, alongside Mark Carey, Callum Coates, Toni Kanal, Damian Quinn, Miles Richardson and Daniel Souter.
According to press material, Ustinov's "largely forgotten play" centres on "the mechanics of toppling governments, the pretences of war and the power of propaganda."
Directed by Robert Laycock, it runs at Southwark Playhouse's new Elephant & Castle home from 28 June to 20 July 2013 (previews from 26 June).
Jimmy Yuill and John Shrapnel will play Banquo and Duncan. Alexander Vlahos (Mordred in BBC's Merlin) will play Malcolm, Norman Bowman (Finding Neverland, Guys & Dolls West End) will play Ross, Ray Fearon (Coronation Street RSC Othello) will play Macduff and Rosalie Craig (NT Shed Table, Finding Neverland) will play Lady Macduff.
The weird sisters will be played by Laura Elsworthy (The Kitchen Sink), Anjana Vasan (RSC Much Ado About Nothing) and Charlie Cameron (The Addicted).
The cast also includes: Andy Apollo, David Annen, Elliot Balchin, Nari Blair, Steven Cree, Jordan Dean, Patrick Neil Doyle, Pip Pearce, Cody Green, Daniel Ings, Harry Lister-Smith, Stuart Neal, Harry Polden, Dominic Thorburn, Katie West and Benny Young.
Co-directed by Branagh and Rob Ashford, Macbeth runs from 4 July to 21 July 2013 at a secret location in Manchester.