BOSTON, England — A few days after Britain voted to leave the European Union, Monika Baginski was in a supermarket, chatting with a friend on the phone in her native Polish, when a man followed her down the aisle. “You foreigner,” Ms. Baginski recalled him saying. “You’ll be out soon.”

Ms. Baginski, 32, said she was stunned. Until that moment, she had never been the target of abuse, even in Boston, a port town on the east coast of England where rancor between longtime residents and the fast-growing population of recent immigrants has been simmering for years.

But since Britain’s referendum vote to leave the European Union, latent hostility toward the new arrivals — most of whom came to Boston from Central and Eastern Europe under rules that let European Union citizens live and work anywhere in the bloc — has burst into the open, many immigrants say. Many in the Latvian, Lithuanian, Polish and Romanian communities in the area are anxiously considering whether they should stay in Britain, or whether they even want to.

“Something is broken in this town,” said Paul Gleeson, a Labour Party councilor in Boston, where 76 percent of voters supported leaving the European Union, the highest pro-“Brexit” proportion in the country. “This veneer of propriety has suddenly disappeared.’’