But none of that is guaranteed.

“Of course I’m worried,” Ms. Luis said, referring to Brexit. “I want to stay here to work and have my career.” She added that friends who had stayed back home were in dead-end jobs, and that “I don’t want to be like that.”

If Britain votes out, someone like her would not be here, and may not be eligible to remain.

Current immigration rules require non-European Union nationals to have graduate-level skill sets and a minimum salary of 20,800 British pounds per year to be eligible for what is known as a Tier 2 visa to work in Britain. The government plans to raise the salary threshold to £30,000, or about $43,000, by next spring.

“The requirement of working in a graduate-level occupation, combined with the earnings thresholds, mean that most jobs in the U.K. labor market do not currently qualify for Tier 2 visas,” the report by the Migration Observatory said.

Even those with high-level skills are making plans in case of Brexit — and even Plan Bs and Cs.

Proficient in five languages, Ms. Martinsone, 34, who is from a rural town in Latvia, started her career at Latvia’s Foreign Ministry but took a sabbatical to pursue a master’s degree in political economy in Britain in 2008.

When the financial crisis struck, she was asked not to return, she said, because the ministry could no longer afford her. She worked for several months in restaurants, but felt embarrassed by having to polish knives and forks. She used her experiences to blog about Britain’s service industry for a Latvian audience.

“It became quite depressing,” she said, “especially as I had just gotten my master’s degree.”

Yet in the midst of tough job market, Ms. Martinsone felt strangely comforted by the knowledge that other workers had good degrees, too. “I felt, ‘I’m not the only one,’ though it did not make me less eager to prove that I could be valued in London.”