Young Vic artistic director David Lan, along with more than 400 theatre professionals, have signed a petition against the imprisonment of UK theatre producer David Cecil.
Cecil was recently released on bail in Uganda after being charged for putting on an unauthorised performance that centred around gay themes.
He is now facing conviction, which could result in two years imprisonment.
Stephen Fry, Michael Sheen, Peter Brook, Michael Boyd and Caryl Churchill are among the list of industry professionals who have shown their support for the campaign led by Lan.
The play produced by Cecil, called The River and the Mountain by poet Beau Hopkins, has been described as a “comedy drama which tackles the controversial interaction of religion, politics, and sexuality”.
It was performed in the Ugandan capital, Kampala, last month.
The petition letter says the play, which presents the killing of a gay businessman by his staff, has been “highly praised for the tragicomic way it attempts to tackle widespread homophobia in Uganda”.
It adds that Lan and his supporters “call on the government of Uganda” to stop the prosecution of Cecil and to “uphold the fundamental right to freedom of expression”.