LONDON — British cultural organizations and prominent figures in theater, dance and film reacted with dismay after Britain voted to leave the European Union. But as with many British industries and institutions, uncertainty prevails over what withdrawal will mean.

People who make their living in the arts had been strong supporters of the Remain campaign, with a survey of members of the Creative Industries Federation showing that 96 percent backed Britain’s membership in the European Union.

“First time I’ve ever felt ashamed and embarrassed to be British … And soon we may have no UK either?” the choreographer Matthew Bourne posted on Twitter on Friday, referring to the possibility of another referendum on independence for Scotland, which voted overwhelmingly to stay within the European Union. “Canada?” tweeted Josie Rourke, the artistic director of the Donmar Warehouse, a London theater.

Michael Ryan, the chairman of the Independent Film and Television Alliance, said in a statement on Friday that the decision was “a major blow to the U.K. film and TV industry.”