LONDON — For years Dover College, on the southeast coast of England, has attracted a steady flow of summer students from across the channel, with parents willing to pay for their children to learn English in a boarding school environment.

Brexit, it seems, has changed that. Enrollment has wilted , and the h eadmaster, Gareth Doodes, has adjusted his future budget in anticipation of a new reality.

“I’ve changed my business model,” said Mr. Doodes, whose school has about 300 day school pupils and boarders within its medieval walls. “We now have more pupils who come to us from non-E.U. countries than before so I don’t find myself in a financial deficit.”

The unending and inelegant debate on how Britain will leave the European Union may rumble on through October, the latest Brexit deadline . But more than 2,000 private schools in Britain and thousands of overseas campuses are tied up in their own debates about how best to prepare for a changed population.