"Central and east European governments hope for a 'reverse brain drain', especially the Baltics, which have experienced substantial outflow of young educated people in recent years," Otilia Dhand, a senior vice president and eastern European expert at Teneo Intelligence told CNBC via email.
"But others, too. For example, Hungary is suffering from labor shortages; most notably health care and IT – exactly the kind of workers that have all left for London," Dhand said.
Estimates by the Office for National Statistics suggest that between the first quarter of 2015 and the same period this year, non-UK nationals from the EU working in Britain increased by 224,000 to 2.15 million
The influx of workers to Britain is believed to have hit a nerve with a number of U.K. voters, with the Vote Leave campaign promising to crack down on immigration.
But with banks like Goldman Sachs predicting a mild recession for Britain in light of the Brexit vote, an economic slump could drive migrants out much quicker than new immigration laws, Richard Jackman, a professor of economics at the London School of Economics told CNBC.
"If there is a recognition that the level of immigration hadn't been much affected by EU freedom of movement, but it's just high because the economy is growing and it's easy to get jobs, then restrictions, in terms of quotas (don't really matter)," he said.