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Prime Minister David Cameron of Britain, second from right, during a campaign visit with farmers near Brecon, Wales, on Wednesday. CreditPool photo by Toby Melville 
LONDON — In a grueling and largely uninspiring campaign, politicians in Britain have struggled to convince voters that Thursday’s general election really matters.
It does — not just for Britain, but for Europe, too.
If Prime Minister David Cameron returns to power, Britain will embark on a fraught and unpredictable discussion about its membership in the European Union, leading to a referendum by the end of 2017 on whether to withdraw from the 28-nation bloc.
Mr. Cameron promised the referendum as a way to placate the right wing of his Conservative Party, which has long railed against the European Union as infringing on British sovereignty and undermining national interests on hot-button topics like immigration.
No country has ever left the European Union (though Greenland, an overseas territory of Denmark, voted to quit the bloc’s forerunner in 1982). Having stood aloof from the first stages of European integration in the 1950s, Britain struggled to get into the club when it changed its mind, finally joining in 1973 and confirming that decision in a referendum two years later.
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But since then the bloc has grown in size and ambition, has created a currency union, and has pushed beyond the more minimalist British vision of a free-trade area.
Britain is today a uniquely truculent and uneasy European partner, one that chose not to adopt the euro as its currency and that finds itself frequently at odds with Brussels over issues like financial regulation.
In European capitals, there is concern about a referendum in a country that many regard as a central part of the European Union, according to Guntram B. Wolff, director of Bruegel, a research institute in Brussels.
“The assessment here is that the U.K. leaving would be not only an economic loss, but also a political and geopolitical loss,” he said.
In a recent analysis, the Bertelsmann Foundation, a German research institute, predicted that, economically, Britain itself would suffer the most from a departure. But it concluded that “the combination of economic and political disadvantages of the U.K. exiting the E.U. would be detrimental for everyone involved.”
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In Britain, many big businesses fret about the risk. In 2013, 45.1 percent of British goods and services exports were to other European Union countries, according to a report by the House of Commons Library.
One worry is that, outside the bloc, Britain would have no influence over the European regulations that companies would ultimately have to comply with in order to trade with the rest of Europe.
A European Union without Britain would be a different place, because the departure of a relatively big, free-market nation would alter its balance of power.
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Ed Miliband, the Labour Party leader, at a campaign event in Colne, England, on Wednesday, the eve of the general election. CreditAndrew Yates/Reuters 
Even a debate over a British exit would most likely encourage anti-European Union parties across a bloc in which support for the longstanding European goal of deeper integration can no longer be assumed.
Greece is teetering on the edge of default, prompting debate over whether the country — and the European Union — might be better off if it left the euro. In France, the far-right National Front wants to quit the euro, and anti-European Union parties are well established in several countries, including the Netherlands. Even in Germany, the bulwark of European integration, a small party, the Alternative for Germany, has made gains by opposing the euro.
Despite the ramifications, Europe has featured little in a British election campaign dominated by the economy, the National Health Service and interminable speculation about political deals that may follow if, as opinion polls suggest, there is no outright winner on Thursday.
The European Union provokes fierce passions among politicians here, particularly on the political right. But the issue resonates much less among voters, for whom it routinely ranks well below the economy, health or education as concerns.
Yet if Mr. Cameron remains prime minister, he will have to deliver his promised “in or out” referendum. Under pressure from those in the right wing of the Conservative Party and the populist U.K. Independence Party, which supports a withdrawal from Europe, Mr. Cameron describes a referendum as a “red line” in any postelection deal.
“I will not be prime minister of a government that does not deliver that referendum,” he told the BBC on Sunday.
If he fails to win a majority, Mr. Cameron may seek support from Democratic Unionist Party of Northern Ireland, which also favors a referendum, or from the centrist Liberal Democrats, whose leader, Nick Clegg, has carefully not ruled one out.
Before a referendum, Mr. Cameron wants to negotiate sufficient changes to the terms of Britain’s membership of the European Union to recommend staying in.
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His main concern appears to be immigration. Mr. Cameron has spoken of restricting welfare payments for Europeans who can come to Britain because the bloc guarantees the citizens of member states free movement across European borders.
But his demands so far remain vague, and he will need the agreement of all the other 27 member states for any fundamental changes in European policy. His ambition of getting changes written into a treaty looks impossible to achieve by 2017. And even if he gets the deal he wants, there can be no guarantee that all in his party would support it, or that he could persuade voters to remain part of the European Union.
Though some polls suggest that Britain would vote to stay, opinion is volatile, and previous surveys have shown a clear majority in favor of leaving.
The opposition Labour Party is against staging a plebiscite now, but it says it would hold one if there were another European Union treaty that transferred further powers away from the British government. That is unlikely during the next five years, but it might be difficult to postpone indefinitely.
By refusing to hold a quick referendum, Ed Miliband, the Labour Party leader, has won support from some who are for the European Union and from big business, which is otherwise skeptical of Mr. Miliband’s interventionist economic instincts.
But some believe that, ultimately, Britain is more likely to remain a member of the European Union if the Conservatives form the next government and hold their referendum.
“You would have the U.K. heavily distracted, almost out of the game, for two years while it focuses on that referendum,” said Robin Niblett, director of Chatham House. “But you have in my view — though I know it’s debatable — an above 50 percent chance that Britain would vote to stay in.”
However, were Mr. Cameron to lose the election and resign, the Conservative Party might well drift to the right and elect a more anti-Europe leader, creating a more difficult environment for any future vote.
“Ed Miliband has promised an in-or-out referendum, he’s just put tougher conditions,” Mr. Niblett said. “At some point, in my opinion, those conditions are going to come to pass.”