The diversion of his work force meant that Mr. Mitchell, a fruit supplier for a major supermarket chain in Britain, lost 50 tons of fruit worth half a million pounds ($680,000) in a matter of weeks.

Mr. Mitchell is not alone in his distress. Similar anecdotes have been reported by a wide range of employers, notably the National Health Service and the hospitality sector. It is a phenomenon tied to Britain’s decision last year to leave the European Union, a process known as Brexit. Since then, thousands of Europeans have already left Britain or have decided not to return, causing a significant drop in migration to the country. Net migration in the year ending in June fell by 106,000, about a third, the government said, “the largest fall in any 12-month period since records began in 1964.”