Alongside Deyn, the show will also star Ed Stoppard and Melanie Gray.
The "deliciously offensive" satire centres on a "yuppie" couple who find their organised lives spiralling out of control when they invite their friend and his young lover over for dinner. The situation then nosedives into a drunken swamp of debauchery.
Deyn rose to fame when she was discovered out shopping by a fashion designer. She has featured on the covers of Vogue, Grazia and Time among many others. She gave up modelling in 2009 to pursue an acting career and has since notched up film credits including The Clash of the Titans.
The Leisure Society will be directed by Harry Burton and produced by Hillscape Productions. The show will run until 24 March 2012.