Should Britain leave and start requiring European citizens to clear the same visa hurdles as other foreign workers, three-quarters of the 2.2 million people from other E.U. countries currently working in Britain wouldn’t make the cut, according to the Migration Observatory at Oxford University. More than 90 percent of the 442,000 European migrants working at British hotels and restaurants also would not qualify.

While European nationals working in Britain make up just 5 percent of the 31.5 million-strong work force, compared to 11 percent from overseas, they have become a visible flash point in the overall debate about whether and what type of immigration really works for Britain.

The “leave” camp argues that it has been too easy for “migrant workers” from Europe to waltz into the country and take British jobs. “We have absolutely no power to control the numbers who are coming with no job offers and no qualifications from the 28 E.U. countries,” Boris Johnson, the former London mayor, said in a recent speech rallying for a Brexit.

British businesses have faced criticism for hiring them. Greencore, Britain’s biggest sandwich maker, drew fire for seeking hundreds of Hungarian employees for a new sandwich factory in Northampton, an hour north of London. Pret A Manger, whose stores dot street corners across Britain, has been faulted for employing relatively few British workers. (A spokesman for Pret A Manger declined to comment.)

Critics also point to the low wages that many E.U. workers seem willing to take in labor-intensive industries, especially people fleeing struggling economies. Nearly 40 percent of the more than two million European workers in Britain hail from low-wage nations such as Poland and Romania. And since a debt crisis struck the European south, growing numbers of Italians, Greeks, Spanish and Portuguese have left for a chance at any employment in Britain.

But for many Europeans grateful to have a job, what is considered a low wage in the eyes of some British is better than what they would get back home. “There are no jobs in Portugal,” said Mr. Graca, who was hoping to be promoted to barista, which pays £9.20 an hour, more than Pret’s base pay of £8.50 and higher than the £7.20 rate considered a living wage. “I’m here to work and earn money,” he said.

Any “out” vote would not force Europeans to leave Britain, at least not right away. For the next two years, the British government would negotiate new treaties with the European Union over labor movement and other matters.

Still, with the referendum looming, thousands of workers across the city are bracing for a potentially murky future. Employers are grappling with uncertainty about whether they will be able to hire Europeans as easily as before.

“What we don’t know is what is going to be the status of those people going forward,” said Keith Howells, the chief executive of Mott MacDonald, a major construction services firm with projects in Britain and worldwide. Around 20 percent of his workers in Britain are from elsewhere in the European Union.

“Will they be welcome or not? Will they be subject to quotas or won’t they?” he said. “It’s potentially hugely destabilizing.”

That’s especially true for London’s restaurants, bars and hotels, since Europeans make up most employees.

A British departure from the bloc “would impact the industry big time, and those who work here,” said Filippo Castellana, an Italian who manages the French restaurant Le Garrick in Covent Garden. On a recent day, patrons were served steak frites and onion soup by staff members from Poland, Latvia, Hungary, Lithuania and France.

“We depend on European workers,” he said. “It would be insane for Britain to leave.”

Around the corner at Suvlaki, a Greek restaurant specializing in grilled meat skewers and stuffed pitas, the owner, Yannis Theodorakakos, was preparing to tally the impact if he needed to obtain work visas for the 13 European citizens working on his staff.

“It wouldn’t be the end of the world,” Mr. Theodorakakos said. A former banker, he expects that an independent Britain would start operating like Switzerland, whose relationship with the European Union is framed by bilateral treaties giving it greater control over immigration. “But if I had to use visas in the future to hire from the E.U., it would cost us money as employers,” he said.

That argument riles backers of the “leave” lobby, who argue that European citizens distort the labor market in part because they are able to come into Britain with virtually no checks and start looking for a job.

Recently, Britain’s popular curry houses aligned themselves with pro-Brexit campaigners, complaining that skilled chefs from places like Bangladesh must get expensive, time-consuming visas while Europeans with little restaurant expertise can work right away. A Brexit would even an unfair playing field, they say.

But to those who claim their business could be crippled without European labor, such talk is a feeble diversion from the elephant in the room in the Brexit debate.

“The fact is we’re doing jobs that most British people don’t want to do,” said Anna Pawelec, the manager of Pillars of Hercules, a 150-year-old pub on Greek Street near Soho that has British owners but is run almost entirely by Poles.

“Most of them wouldn’t get out of bed for the money we earn,” added Ms. Pawelec, standing behind a row of beer taps as the song “We Didn’t Start the Fire” blared from loudspeakers.

“Foreign people work hard,” she added. “We contribute hugely to this country. So everyone is thinking the same thing: Don’t tell me to leave.”