LONDON — Europe was pummeled by crises from start to finish in 2015, with terrorist attacks, bankruptcy brinkmanship and an unparalleled refugee influx combining to leave continental unity in tatters by year’s end.

But instead of relief, 2016 could bring an unraveling.

In addition to the flash points of the past year — all of which are poised to flare again — Britain is likely to throw fresh instability into the mix with a referendum on whether to leave the European Union. Once judged an unlikely prospect, many observers now see a 50-50 chance that populist-minded, immigration-fearing British voters will elect to cut this island nation adrift from a continent beset by existential struggles.

If they do, it would mark the first time in the E.U.’s history that a country has chosen to withdraw, reversing what had been seen as an inexorable expansion of the pact credited with bringing peace and stability to the historically bloody lands of Europe.

The Syrian conflict has created the largest wave of refugees to hit Europe since World War II. View Graphic

The Syrian conflict has created the largest wave of refugees to hit Europe since World War II.

A British exit could hasten a broader E.U. breakup, with continental leaders despairing that an already strained union may struggle to survive without one of its cornerstone members. Washington, too, has much to lose if the country that has traditionally bridged the Atlantic divide opts to sail off into the icy depths of the North Sea. And the United Kingdom itself could fall apart if Britain chooses to leave, with pro-E.U. Scotland likely to revive its demand for independence.

But all of that may not be enough to outweigh the anxieties of British voters who gaze across the English Channel and see nothing but trouble.

As Europe’s crises have multiplied over the past year, the once-overwhelming share of British voters who favor staying inside the E.U. has dwindled — with some polls showing the contest dead-even. And the “out” campaign has room to grow if Europe’s problems persist, as most analysts expect they will.

“Given that by any objective measure the E.U. is in a terrible mess, I’m shocked that the ‘in’ campaign is still getting half,” said Charles Grant, director of the London-based Center for European Reform.

Grant said he wants to see Britain remain part of the E.U., but he is pessimistic that it will. Fears about immigration explain why.

“It’s always quite easy to scare people,” Grant said. “If the British vote to leave the E.U., it will be because of worries about migration and refugees.”

Britain has largely insulated itself from the historic exodus of millions of people fleeing the war zones that ring Europe. It has opted out of an E.U.-wide refugee-relocation program and has used the 19 miles of water that separate this nation from the European mainland as a barrier to those who try to make it here on their own.

But anti-E.U. campaigners have conflated the refugee issue with a record level of net-migration to Britain, much of which is fueled by European citizens moving here for economic reasons. Under the E.U.’s free-movement principle, Britain can’t stop them, prompting “out” advocates to argue that the country has lost control of its borders and can only get it back by ditching the E.U.

The more that Europe has struggled with its management of refugee flows — and with other thorny problems, including terrorism and debt — the more confident anti-E.U. advocates have become that they will prevail.

“The momentum is on our side,” said Nigel Farage, leader of the U.K. Independence Party and the country’s most prominent E.U. opponent. “For those of us who believe in nation-state democracy, 2016 is a very bright dawn indeed.”

A British vote to leave, Farage proclaimed in a December speech on the floor of the European Parliament, would mark a “tipping point” that could doom the E.U. — an outcome that the bombastic former commodities trader has made clear he would welcome gleefully.

It was political pressure from Farage and from Euro-skeptics within Prime Minister David Cameron’s own Conservative Party that led him to promise a referendum in the first place. At the time, in January 2013, a British vote to leave seemed improbable.

Now Cameron is locked in delicate negotiations with his fellow E.U. leaders that could determine whether Britain stays or goes. The prime minister has vowed he will lead the campaign to keep Britain within Europe “with all my heart and soul,” but only if he can extract meaningful concessions that will give the E.U. less influence over British affairs.

Cameron’s demands include permission for Britain to opt out of the E.U.’s founding ambition to “forge ever closer union”; greater power for national parliaments to block E.U. legislation; and formal recognition that the euro isn’t the union’s only currency.

European leaders have signaled that they’re willing to deal on those issues. But Cameron’s fourth demand — a restriction on benefits for immigrants from within the E.U. — is far trickier. As German Chancellor Angela Merkel and others have pointed out, such a move would violate core E.U. principles that bar discrimination on the basis of nationality.

The issue is critical if Cameron wants to show he’s serious about reducing immigration to Britain — a promise he’s repeatedly made but has been unable to fulfill. And yet, with only weeks to go until a critical E.U. summit, there’s little indication of how negotiators can break the deadlock.

“Cameron can’t go into the referendum with nothing on this,” said Stephen Booth, co­director of the London-based think tank Open Europe. “But what will the compromise be? We really don’t know.”

Despite the uncertainty, Cameron has said he wants to make a deal by February and has hinted that the referendum could come as soon as this summer.

After making his case for reform to fellow E.U. leaders over dinner in Brussels in late December, he told reporters that “2016 will be the year we achieve something really vital, fundamentally changing the U.K.’s relationship with the E.U. and finally addressing the concerns of the British people about our membership.”

But it could also be the year that divides his party — and costs him the premiership. If Cameron leads the “in” campaign and loses, he will come under pressure to resign just a year after leading the Conservatives to a commanding victory in national elections.

Cameron’s own cabinet is divided on the Europe question, and at least some of his ministers are expected to campaign for an exit, although none have shown their hand.

One person who has made his views known is President Obama, who told the BBC last summer that Britain’s E.U. membership “gives us much greater confidence about the strength of the transatlantic union.”

Without Britain, the E.U. would be greatly diminished, having lost the world’s fifth-largest economy and military. It would also take Europe’s focus away from its other struggles, which continue to demand urgent attention.

“The E.U. has got enough on its plate right now,” Booth said. “It doesn’t need one of its biggest and most dynamic members leaving.”