Jeremy Herrin has called for arts organisations to have their funding cut if they fail to improve diversity.
The Headlong artistic director said Arts Council England should target companies who had not made progress by the time of the next funding round.
Herrin also said that the industry needed “systemic change” if it was to improve accessibility, both for audiences and for those wanting careers in the arts.
He said Arts Council England was encouraging national portfolio organisations to become more diverse, but was not yet being punitive.
“What I would suggest there, is push it this funding round, and then next start making cuts if people aren’t stepping up to it, because I think that’s enough time for these organisations to sort themselves out,” he told an audience at Soho Create festival in central London.
ACE unveiled a new diversity strategy in 2014, under which national portfolio organisations are monitored on how well they reflect diversity in the communities they serve.
This will be “a way of holding them to account”, the Arts Council said at the time .
The People, Places and Things director was speaking at a discussion event about the show alongside Denise Gough, who is starring in the production in the West End.
He went on to say that the industry required an overhaul in the way it approaches diversity if it is to progress.
“What we need is systemic change. That’s why we need to talk about it. The fact is that for a lot of girls, theatre has nothing for them. A lot of young black, Asian and minority ethnic kids don’t want to go to the theatre because they can’t see themselves,” he said.
He added: “We just need to invest in change, and absolutely make sure that it’s not just one white, middle-class male, often university education, often Cambridge, being recognised. Our culture is diverse and our storytelling should reflect that.”
Soho Create  continues until June 10.