Following two successful runs at Ovalhouse last year, The Act is transferring to Trafalgar Studio 2 next month for a five-week season.
The play, billed as a "ground-breaking cabaret-style production comprised of personal anecdotes, verbatim House of Commons speeches and song", centres on the 1967 decriminalisation of homosexuality.
Baldwin's theatre credits include adult pantos Jack Off the Beanstalk, Get Aladdin, Sleeping Beauty and Robin Hood (Above the Stag Theatre), and Westward Ho (White Bear Theatre).
Hescott trained on the National Theatre Studio Directors Programme, with recent credits including the National Youth Theatre's West End revival of Tory Boyz by James Graham.
The Act runs at Trafalgar Studios 2 from 28 February to 29 March 2014 (previews from 25 February).