Check out the latest in immigration news.

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LEICESTER, England — Thabata Martins says she sent out her résumé more than 100 times in the year after finishing her studies to become a nurse in Spain in 2013.

“It’s not Málaga. We don’t have the beach, we don’t have the sun every day, no beach bars — but the people are very nice here,” Ms. Martins said. At long last, she said, she can perform the job for which she trained.

In Spain, Ms. Martins, 25, is part of a generation of young Europeans forced to move far from their economically struggling home countries to find employment. But in Britain, where the economy has rebounded more strongly than on the Continent — the unemployment rate stands at 5.7 percent, compared with 9.8 percent in the European Union and 11.2 percent among the 19 members of the euro currency union — she is part of an influx of foreign workers that has intensified a long-running debate over immigration.

On Wednesday, the U.K. Independence Party, the populist, right-wing party that has put curbing immigration at the heart of its agenda for the national election in May, said Britain’s goal should be to reduce immigration to 20,000 to 50,000 people a year, down from nearly 300,000 last year.

But what is happening in Leicester represents a twist in that debate: Even as opposition to immigration grows, British employers in some fields are actively recruiting workers abroad, saying they often cannot fill jobs within the country.

That was the case with Ms. Martins, who was encouraged to come by Leicester’s health officials. They have a two-year program to bring 500 nurses to the city from Spain, Portugal and Ireland, more than half of whom have arrived.

And health care is just one of the economic sectors scrambling for workers. Last year, Greencore, a sandwich maker that supplies many of Britain’s grocery stores, announced plans to recruit in Hungary.

Greencore cited high employment rates near its new factory in Northampton, saying that not enough locals wanted jobs that required working early mornings or late nights. The response of The Daily Mail newspaper was a front-page headline reading: “Is there no one left in Britain who can make a sandwich?”

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. UnderEuropean 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.

Christopher Slay, managing director of Skills Provision, a recruitment agency based in Somerset, in southwest England, praised the work ethic and attitude of young East Europeans. By contrast he recounted the case of a Welsh youngster, recruited for factory work, who responded to criticism by saying: “You don’t think I’ve come to work just to be told what to do, do you?”

Mr. Slay said that a recent increase in the number of apprenticeships had improved matters. But he added that jobs involving night and early-morning shifts, like the ones at Greencore, could be hard to fill. “If you are the boss of a company, are you supposed to shut up shop because you can’t find British people prepared to get up at 6 a.m.?” he asked. “Or do you look for alternatives?”

Critics of overseas recruitment come not just from the populist right, including the U.K. Independence Party, but also from the center-left. David Goodhart, the author of “The British Dream,” a book critical of immigration policy, argues that plentiful foreign labor “breaks a social contract in Britain and reinforces many of the weaknesses of the British economic structure, such as short-termism and lack of training.”

It was after Poland and seven other former Communist nations joined the European Union in 2004 that immigration became especially sensitive in Britain. Along with Sweden and Ireland, Britain opened its labor market fully to the new countries, while France, Germany and others applied temporary controls to limit numbers.

A study commissioned by the British government before the 2004 European Union expansion hugely underestimated net immigration from Eastern Europe, suggesting 5,000 to 13,000 arrivals a year up to 2010. The 2011 census identified 521,000 people born in Poland as British residents, the vast majority of whom arrived after 2004.

More recently, Britain’s growing economy has encouraged workers from Spain, Italy, Portugal and Greece to relocate here.

That is good news for Maria McAuley, assistant chief nurse at University Hospitals of Leicester. The hospital group employs more than 4,000 nurses, including Ms. Martins, at three sites, and struggles to replace the 200 or so who retire or leave each year.

It is hard to argue that Ms. Martins is a burden on Britain. Her education and training was paid for in Spain, she speaks excellent English, and she does a job her employers could not fill at home, even though everyone who qualifies as a nurse in Leicester is guaranteed a job if they want it.

And while many Britons seem to resent the idea of immigration, they nonetheless rely on it. Without international nurses, Ms. McAuley said, the hospital would probably have to cut back on operations.

“We wouldn’t be able to continue business as normal,” she said. “The risk would be too great for the patients.”