February 25, 2016 6:57 AM EST

Perhaps U.K. Prime Minister David Cameron believed back in 2013, when he promised a referendum on whether Britain would stay in the E.U., that Euroskeptics couldn’t possibly win. But much has changed since, and though a majority of those voting in the June 23 referendum are likely to want to keep Britain in the union, the risk is real that a surge of fear over migrants, or a terrorist attack, could tip the scales toward an “out” vote. And that would have major implications for Britain, Europe and the world.

A vote to leave would force the British government to renegotiate trade and investment relationships with other E.U. members. Over time, Britain might secure access to E.U. markets for its goods on fairly favorable terms, but European leaders would make the process as arduous and painful as possible to discourage other E.U. states from threatening exit to win concessions. Two years of negotiations–at least–would generate enough uncertainty to create serious problems for Britain’s growth and investment outlook.

It would prove much more difficult to win access to European services markets. In the financial sector, E.U. leaders aren’t likely to accept a continuing role for London as the major financial center in Europe, particularly for euro-zone financial products. Brexit might carry a heavy political cost as well, because it could give Scottish nationalists the argument and energy they need not only to hold another vote on Scottish independence from the U.K. but to win this time.

Brexit would also damage Europe, especially at first. In time, it’s possible that a U.K. exit would make it easier for E.U. leaders to move forward with treaty changes, traditionally resisted by the British, that would allow for closer union, possibly even of fiscal policy. In the meantime, however, losing Britain would hurt. The U.K. is the second biggest contributor to the E.U.’s budget, after Germany. Losing the U.K. could cost the E.U. 15% of its GDP.

More worrisome, Britain is not the only E.U. member ambivalent about staying within the union. The Brexit precedent could pose a major threat to Europe’s open borders, the euro zone, even the entire European project. It would surely weaken efforts to strengthen damaged European-U.S. ties and undermine efforts to complete a historic transatlantic trade-and-investment agreement.

In the end, a majority of British voters will probably choose to stay in the E.U. But this is no sure thing. London Mayor Boris Johnson announced on Feb. 21 that he will support a vote for Brexit, and though his calculation is surely driven more by a bid to win Conservative Party support to become Prime Minister than by any genuine conviction, he’s playing with fire. When it comes to Brexit, no one can be confident of the outcome.

This appears in the March 07, 2016 issue of TIME.

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