A few months ago, London-based lawyer Yves Elbaz went rummaging through his papers for tax and banking documents and began drafting his application to Britain's immigration authorities. With the country due to vote this Thursday on whether it should leave the European Union, the Canadian-French national wanted to make sure he could stay.

"I love the thought of living every day on an island, where the foundations of the English-speaking world started," the 36-year-old says.

Like others who hold EU passports, Elbaz arrived in Britain without a visa and didn't need to bother with one before he started his job. But that principle of free movement may have to be renegotiated or even abandoned in favor of a new visa regime if voters favor a British exit, or Brexit, from the 28-member bloc.

The estimated 3 million or so EU citizens living in Britain aren't likely to be thrown out overnight, but they could be faced with new rules and new paperwork — potential restrictions that have made many anxious, according to immigration lawyer Colin Yeo.

Some "leave" campaigners have said that people who are already established in Britain don't have anything fear, while others have suggested introducing a work permit system that could mean only skilled workers in professions where there are shortages will be allowed to stay.

"In the last two months I've met quite a few who are very worried about their position in this country," said Yeo, a barrister with London's Garden Court Chambers. "I've heard from other immigration lawyers who're seeing the same thing."

One of those who are concerned is Katarzyna Kowalska, a 35-year-old cleaner from the central Polish town of Pulawy. She's among the hundreds of thousands of Poles who flocked to Britain in the wake of her country's 2004 accession to the EU and has been in London for 11 years, but only recently started her immigration paperwork — a precautionary move.

"They are threatening us with Brexit and I'm afraid I may have problems crossing the border, coming and leaving, if it happens," she said in a telephone interview. "London has become my second home. I have a good job. I have friends here. I want to live here."

European citizens are able to begin the process of applying for British citizenship after five years of continuous residency in the U.K., or less if they're married to a British national. The process can take up to a year, depending on the circumstances.

So far, the evidence of a rush to secure British passports is anecdotal. The phenomenon is too recent to be captured in official statistics and Britain's Home Office said it wouldn't comment on any matter linked to the referendum.

The latest figures show that the number of EU nationals seeking British passports has yo-yoed in the past few years between 10,000 and 20,000 — a fraction of the total thought to be living in the country.

That may be because an EU passport already allows free access to work, health care, education, state pension and local elections. European citizens even wait in the same line as their British counterparts at the airport.

Under the circumstances, there has been little incentive for most EU nationals to fork out the hefty fees involved in acquiring British nationality, which can easily reach 1,400 pounds ($2,000) or more.

But that calculus may change after Thursday, when the British voters go to the polls to decide whether or not to bid goodbye to their European partners.

Yeo said one thing was for sure: "Brexit will be great for immigration lawyers."

But he quickly added that he didn't want the work.

In immigration law, a British exit from Europe would mean "a legal mess that could take years to sort out," he said.

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Scislowska reported from Warsaw, Poland.