Leading figures in British theatre have condemned “sexual harassment or abuse of power” within their industry.

Emma Rice, the artistic director of Shakespeare’s Globe, and Rufus Norris, the National Theatre’s artistic director, are among the signatories to the statement, which says there “can be no place for sexual harassment” in the world of theatre.

The statement comes after allegations of sexual misconduct by the US film producer Harvey Weinstein prompted a blizzard of related claims on both sides of the Atlantic. On Friday the Guardian revealed one of the most influential directors in British theatre, Max Stafford-Clark, was forced to stand down from the company he founded after being accused of inappropriate, sexualised behaviour.

Stafford-Clark – the former artistic director of London’s Royal Court theatre – was forced out of the Out of Joint after a formal complaint that he made lewd comments to a member of staff. Stafford-Clark said he “wholeheartedly” apologised for “any inappropriate behaviour that made some former colleagues feel uncomfortable”, adding that it was never his intention to bully or harass.

“Following the reports and allegations of the last two weeks, first in America and, more recently, closer to home, we have come together to make clear that there can be no place for sexual harassment or abuse of power in our industry,” said the statement signed by the heads of 19 theatres.

Facebook Twitter Pinterest Max Stafford-Clark was accused of inappropriate, sexualised behaviour. Photograph: Tony Larkin/Rex/Shutterstock

“We salute the bravery of everyone who calls out this abusive behaviour. We support a theatre culture that empowers people to speak up: a culture where abuse of power is always challenged.

“We are committed to working together to ensure that theatre is a safe space for all, where everyone is respected and listened to. The Royal Court theatre’s day of action on Saturday 28 October is one important part of this process. Together, we are developing further ways to support people to speak up and to hold others to account.

“It is the responsibility of the industry to create and nurture a culture where unacceptable behaviour is swiftly challenged and addressed.

“We want to be absolutely clear and say again: there is no room for sexual harassment or abuse of power in the theatre. Everyone deserves to enjoy a happy, healthy and safe working environment. We will support you to speak out, and we will hear you when you do.”

The statement was also signed Rupert Goold, artistic director of the Almeida theatre, Nicholas Hytner and Nick Starr, who recently set up the Bridge Theatre, and Josie Rourke of the Donmar Warehouse.