LONDON — (CNN) The British pound slumped to its lowest level in 31 years on Tuesday on fears that the U.K.’s divorce from the European Union will be bad for the economy.

The currency fell to just above $1.27 in early trading, lower even than in the immediate aftermath of the EU referendum on June 23, when Brits voted to take their country out of the 28-member group.

Brexit plans have begun to emerge in the last few days: talks with the EU will begin in early 2017, the exit will happen two years later, and the U.K. will place a high priority on controlling immigration.

European leaders have made clear that if Britain does not allow free movement of EU citizens across its borders, it will lose some of its rights to access the free trade area.

So investors are worrying again about two big issues: British exporters may find it harder to compete in Europe, and the country’s banks could lose the ability to do business freely across the region.

Thousands of financial firms in the U.K. currently have “passports” that allow them to trade in Europe without establishing subsidiaries in each country. And those businesses are vital for Britain: the financial and related services sector accounts for 12% of GDP.

Bloomberg reported Tuesday that Prime Minister Theresa May would “refuse to prioritize” the financial services industry in exit negotiations with the EU. Citing three anonymous government sources, Bloomberg said the sector held far less sway with May than with her predecessor David Cameron.

Instead, May now appears to be putting control of Britain’s borders first. Brexit campaigners had promised to impose new limits on the number of EU citizens entering the U.K.

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“We voted to leave the European Union and become a fully independent, sovereign country,” the Conservative leader told party members this weekend. “We are not leaving the European Union today to give up control of immigration again.”

Kit Juckes, a strategist at Societe Generale, said that May appears to be treating immigration as “the hardest of lines… [that] won’t be sacrificed or watered down in order to keep access to the single market, particularly for financial services.”

Some investors fear that the strategy will result in a “hard” exit from the EU and years of pain for Britain.

The U.K. economy has proved more resilient than expected in the wake of the EU referendum, but the sharp fall in the value of the pound and a big injection of money from the Bank of England have helped limit the fallout.

Treasury chief Philip Hammond acknowledged Monday that the British economy would pay a price for Brexit.

He confirmed that a target to balance the budget by 2020 set by his predecessor would have to be abandoned — a consequence of Brexit that will add to Britain’s £1 trillion-plus debt.

The pound has lost fallen than 15% over the past year, and is now trading way below its recent high of $1.71 set just two years ago. Analysts at UBS said the pain is far from over.

“In our view it is only a matter of time before less positive data starts to appear,” they warned.

The-CNN-Wire ™ & © 2016 Cable News Network, Inc., a Time Warner Company. All rights reserved. (PHOTO: CNN Money)