Following a 2010 launch in an empty shopping unit in Elephant and Castle, Theatre Local presented Debbie Tucker Green's truth and reconciliation and the world premiere of Rachel De-Lahay's The Westbridge in Peckham last year.
The scheme, which was established to take plays to "alternative spaces", will return to former small arms and cricket bat factory on Rye Lane, opposite Peckham Rye Station, which was saved from demolition thanks to community group Peckham Vision.
It stars Lucian Msamati playing a British MP. Following a controversial defeat at the polls, he returns to Nigeria and enters a political battle that makes him question what he believes and where he truly belongs.
The production, which opened at the Royal Court on 26 March (previews from 22 March) continues until 14 April. The show is designed by Tom Piper with lighting by Stephen Andrews and sound by David McSeveney.
Vera Vera Vera will run from 4 to 28 July at the Bussey Building.