Stephen Fry and Sting have threatened to quit the Garrick Club unless members vote to admit women.
The actor and the singer have signed a letter with Dire Straits frontman Mark Knopfler pledging to end their links with the historic institution if it remains men-only.
Theatre, film and television producers also signed the document, which warned members were in an untenable position because of 'very public controversy' over the issue.
Broadcaster John Simpson said he and many others 'would also find it impossible to stay' if the 193-year-old London club does not open its doors to women.
The Garrick's 1,300 members, who include King Charles, deputy prime minister Oliver Dowden and actor Hugh Bonneville, are due to vote at a special general meeting on Tuesday.
TV icon Stephen Fry, one of 1,300 members with the historic club, threatened to leave
Sting (pictured 2023) is among those threatening to quit unless the club admits women
The Garrick Club members-only organization in London, UK, on Wednesday, March 27, 2024
The letter to chairman Christopher Kirker was signed by theatre producer Karl Sydow and Matthew Byam Shaw, an executive on Netflix's The Crown.
It said: 'The current very public controversy over this issue has put us all in an untenable position.
'Our relations with female artists, co-producers, authors, cast members, members of our creative teams, backstage and front of house theatre staff have all been jeopardised by the recent publicity to the point that, without serious progress being made to finally address this anomaly, we won't feel able to continue as Garrick members.'
The Garrick was founded in Covent Garden in 1831 as an organisation for actors, theatre patrons and 'men of refinement'.
Women are allowed in only if they are invited by a member and accompanied by a man throughout their visit.
Several high-profile members quit earlier this year including the head of the civil service, Simon Case.