According to the Recruitment & Employment Confederation, a professional body for the recruitment industry, British employers struggle to fill jobs in engineering and computing — but also in construction, hotels and catering. Truck and delivery drivers are in short supply (partly because of the cost of getting licenses) and shoppers wanting home deliveries before the holiday season last year were warned by a government minister to buy early.

For many employers, the solution is across the Channel. Under European Union rules, any citizen of the 28-nation bloc can work in Britain without a permit (except, for now, Croatians, whose nation joined only in 2013).

Many people say access to this pool of labor is vital to Britain’s flexible labor market, and crucial to the country’s recent economic recovery. “It is difficult to see how Britain could be a successful open economy without being reasonably open to immigration,” argued Jonathan Portes, director of the National Institute of Economic and Social Research.

“Most economists think that immigration is broadly positive for the British economy,” he said. “There may be some negative impact on wages at the lower end of the employment scale, but even the evidence for that is pretty weak.”

European immigrants are generally less likely to claim welfare than those born in Britain and, last year, a report by two economists at University College London said they made a substantial net contribution to British public finances from 2000 to 2011.

Britain has recruited foreign nurses since the 1930s, and has exported them too, including to the United States. But Britain is now a net importer of nurses, according to the Royal College of Nursing, which represents the profession here. The group blames insufficient training schools and relatively low pay.

More controversial are the semi- or low-skilled jobs that often go to foreigners. In 2013, the celebrity chef Jamie Oliver said that without migrant workers, he would have to close some of his restaurants. Young British workers were “wet behind the ears” and European immigrants were “tougher” workers, he said.