The show's producers Snapdragon Productions are giving away 20 tickets for the matinee performance, which will be allocated to vendors of The Big Issue magazine.
Guests will also have a tour of the recently opened venue and a post show chat with the producers and members of the cast.
Snapdragon's Sarah Loader said, "I'm delighted that we will be welcoming The Big Issue Foundation and the vendors they support to the Park Theatre to see Thark on Saturday. The Foundation does fantastic and important work and we feel privileged to be a part of it."
Thark, which is adapted from the classic Ben Travers farce by Clive Francis, finishes its run on Sunday (22 September 2013).
TV stars raise awareness in exhibition
Another initiative supporting the fantastic work of The Big Issue Foundation is a new photography exhibition which opens tomorrow (18 September) at the Gallery in the Crypt, St Martin-in-the-Fields.
Stars from TV series including Skins, The Borgias, Glee and Waterloo Road have posed as rough sleepers for the exhibition, which aims to "challenge the public not to ignore rising levels of street homelessness".
Prescott said: "Most people are no longer shocked when they see someone living on the streets. In fact, many people simply walk by without so much as a second thought. I can't imagine a single person doing so if walking past a person they even faintly recognised from some area of their own life, past or present, in a similar state."
Big Issue Foundation CEO Stephen Robertson added: "The homeless population is shockingly on the increase. As the street population swells we are all challenged as citizens to not turn away, to ignore and pigeon hole people as 'unworthy'. This exhibition brilliantly asks us to think again and to decide just what makes us care. Do our stereotypes and assumptions about others help us to maintain an unrealistic view of people in the modern world?"
The exhibition is free, and prints will be sold to support the The Big Issue Foundation and youth homelessness charity Centrepoint.