Sir Ian McKellen, Dame Julie Walters and Sir Patrick Stewart are among a group of British actors calling on Boris Johnson to resolve the issue of visa-free EU travel for artists.
More than 100 Equity union members have signed an open letter describing the new Brexit rules as a "towering hurdle" for the industry.
It follows a similar statement published in January from music artists including Liam Gallagher, Sir Elton John and Ed Sheeran, as well as Glastonbury co-organiser Emily Eavis, criticising the government for failing to act.
And more than 280,000 people have signed a petition calling for a cultural work permit deal to be reached between the government and the EU.
The Digital, Culture, Media and Sport (DCMS) Committee is today due to hold a one-off session on the government's handling of negotiations.
First published in The Guardian newspaper, the actors' letter says that those working in the performing arts have already lost work.
"Before, we were able to travel to Europe visa-free," the statement says. "Now we have to pay hundreds of pounds, fill in form after form and spend weeks waiting for approval – just so we can do our jobs."
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Since the UK left the EU and free movement ended, performing artists hoping to tour must now seek separate permits to work in many of the 27 member states.
They will also have to pay for expensive carnets (permits) to cross borders with equipment and trucks carrying kit, or they could have their journeys capped.
The industry has already been badly hit by the COVID-19 pandemic, with the majority of venues closed in 2020.
Other acting stars who have signed the latest letter include Miriam Margolyes, Anne-Marie Duff and Celia Imrie.
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"For a sector that is deeply embedded in the international community – from touring theatre and dance to film, television and commercials – which must work fast, flexibly and to demand, this is a disastrous blow and will hit those already struggling and marginalised groups the hardest," it says.
"Prime minister, we urge you to negotiate new terms with the EU, allowing creative practitioners to travel to the EU visa-free for work, and for our European counterparts to be able to do the same in the UK.
"Not acting now will do further and irreparable harm to the UK's creative workforce, our industries and to our standing on the international cultural stage."
Alongside the list of signatories, members of the trade union for creative practitioners have been emailing their MPs to lobby on the issue.
Equity general secretary Paul W Fleming said: "Art and entertainment are a British success story. Worth more to our economy than banking, government intransigence threatens a cornerstone of our international soft power and a key export.
"More than that, the language of art and entertainment knows no boundaries; freedom of movement for our members as artists and working people is achievable, desirable and essential."
In a statement to the Guardian, a UK government spokesperson said they were "working urgently with our cultural sectors to resolve any new barriers" artists face so that touring can resume "as soon as it is safe to do so".