British prime minister David Cameron said on Sunday that his government will insist on a review of the free movement of people within the European Union.

“I believe in the single market, I believe in free movement,” he said on the BBC’s The Andrew Marr Show but also pointed out, “We’ve got so many unemployed people in our country that we want to train and educate and give apprentices to and get back into work” while companies are hiring workers from other European countries.

Home Secretary Theresa May told The Sunday Times that she is worried that an expansion of the European Union and its freedom to travel between member states will increase labor migration to Britain. “We are looking at this whole area of the abuse of the freedom of movement,” she said.

When restrictions on workers from Bulgaria and Romania are lifted in 2014, Western European nations expect to see an increase in labor migration from those countries. But as has been the case with Central and Eastern European member states that joined the border-free Schengen Area earlier, the ability to work in richer European nations causes incomes to rise dramatically in the home countries. As labor demand has also weakened in the core European states in recent years, labor flows have decreased.

Poland is a case in point. Since it entered the Schengen Area in 2004, incomes there have risen more than a third. According to estimates from the Polish government, the number of Poles staying temporarily in other European countries more than doubled between 2004 and 2007 to nearly two million. Even before the 2008 banking crisis and subsequent debt crises in Europe, migration flows, particularly to the United Kingdom, were weakening though.

A 2008 Institute for Public Policy Research study estimated that up to half of Central European labor migrants, most of them from Poland and the Baltic states, had already left Britain again with the pace of departures accelerating that year.

Britain isn’t actually part of the Schengen Area like the rest of the European Union but does allow workers from the continent unfettered access to its shores and labor market. Curbing the free movement of people in Europe would undermine one of the key pillars of the community which especially peripheral member states are likely to resist.

In the improbable event that Britain succeeds, however, writes The Guardian, “France would probably demand an end to the free movement of services,” a vital British interest.