WASHINGTON — Brexit is winning — that is, Britain’s exit from the European Union. As the June 23 referendum approaches, public opinion has swung toward “Leave” the EU as opposed to “Remain” in the EU. This has fueled anxieties about the global economy and the fate of Europe.

Brexit could compound economic pessimism, leading to a selloff in stock markets and a further slowdown in global growth. The long-term worries include a gradual breakup of the EU if Brexit triggers similar votes in other EU members, “where public confidence in the EU … is at a record low,” warns a memo from the Institute of International Finance, an industry research group. Scotland might also demand a new independence referendum.

The shift in public opinion is unmistakable. In a conspicuous reversal, the Financial Times “poll of polls” now has “Leave” overtaking “Remain” by a 47 percent to 44 percent margin. In some surveys, the gap is much larger. A poll taken for the Independent newspaper has Leave at 55 percent (up four percentage points since April) and Remain at 45 percent (down four percentage points).

“What has happened is that the Leave side — having lost the economic argument — has succeeded in making the debate about immigration,” says Jacob Kirkegaard of the Peterson Institute for International Economics, a Washington think tank. This has always been Brexit’s “strongest political card,” he says, because the government, hamstrung by EU law, has been unable to stop surging — and unpopular — inflows.

Prime Minister David Cameron, Brexit’s leading opponent, had pledged to reduce annual immigration to less than 100,000, says Kirkegaard. Instead, it zoomed to 333,000 in 2015. About half the immigrants come from Eastern Europe (Poland, Hungary) and are covered by EU law, which permit citizens of its 28 members to settle in any of the others. The remaining immigrants — heavily from India, Pakistan and other remnants of the British Empire — are regulated by United Kingdom law.

Still, Kirkegaard thinks that Remain will prevail. He’s not alone. Despite the polls, bookmakers’ odds that Leave will win are “only around a third,” reports Capital Economics, a consulting firm. There seem to be two main reasons for this.

First, many Brexit opponents believe there’s an automatic correcting mechanism at work. As Brexit’s popularity increases, financial markets become jittery and this triggers a backlash. Stocks and the pound lose value. Wavering voters are reminded of Brexit’s economic costs and shift from Leave to Remain.

The economic costs could be considerable. Some economists think the pound could fall 10 percent to 20 percent in value. By making imports more expensive, this could increase inflation and erode the purchasing power of wages.

Nor is that all. The UK sells nearly half its exports to other EU countries. This commerce would be disadvantaged if UK exporters have to pay higher tariffs imposed on nonmember countries. For that reason, the UK would also become less attractive for new factories and corporate offices aimed at serving the entire EU market. Similarly, London’s status as Europe’s main financial center would be challenged.

Second is faith that a last-minute focus on undecided voters will produce a surge for Remain. Curiously, the struggle isn’t partisan. Cameron’s conservative party is bitterly split, and many of its leaders are campaigning for Brexit. Likewise, many Labor voters support staying in the EU, and Gordon Brown — a former Labor prime minister — is working hard to defeat Brexit.

Brown has compared Britain’s flirtation with Brexit to America’s infatuation with Donald Trump. The assumption is that both are flights of fancy and that, for Brexit, once in the privacy of the voting booth, people will come to their senses and stick with the EU.

Whether that happens remains to be seen. What is clear is that Brexit would simply be the first step in a long contentious process. Negotiating a new trade agreement “would take at least five years … and without any guarantee of success,” Donald Tusk, president of the European Council, warned last week. If Brexit wins, both supporters and opponents may be disillusioned.

Robert Samuelson is a columnist with The Washington Post.