This worries Dr. Auzinger, who has to hire 407 nurses and doctors for the hospital’s new intensive care wing. Last month, not a single European applied for an advertised position as a senior consultant. “Before, at least a third of applicants were European,” he said.

Dr. Auzinger is happy to hire qualified Britons. “But there are not enough doctors and nurses in this country,” he said. “The numbers being trained do not cover the needs.”

In March, the government announced a plan to hurriedly train more British nurses. Yet in September, enrollment at nursing schools dropped, because the government also cut grants to nursing students. That is one reason Peter Absalom, associate director for recruitment at King’s, is now trying to replace one immigrant group with another. “We are looking to the Philippines, Australia and India,” he said. Three major recruitment drives are planned over the next 12 months.

Every time Mr. Absalom hires someone from overseas he has to pay for their visas and a collection of other charges, which add up to more than £4,000 per person over three years. It can take a year before the nurses start work. Europeans could be hired with no visa costs and no extra paperwork. Over the last five years, nurses from Portugal, Spain, Ireland and other European Union countries have accounted for about a third of the total intake.

Now King’s has stopped its hiring campaigns in the European Union.

“What is particularly difficult is that we cannot give candidates any certainty on their future status,” Mr. Absalom said.

Dr. Auzinger has been in London for 18 years. He, too, would consider going back to Austria if he could transplant his job there, but he cannot. He thinks the way Brexit is affecting the N.H.S. is symptomatic of a poor treatment plan. Britain is ailing. People are angry. Brexit was the treatment offered to them. What worries Dr. Auzinger is the lack of a diagnosis.