Prime Minister David Cameron has faced off against the 27 other EU leaders, telling them to grant Britain a new deal to settle the festering issue of their relationship or face a possible divorce as soon as this summer.
Cameron said he was "battling for Britain" at a Brussels summit - and for a less intrusive EU that would benefit other countries, too.
But French President Francois Hollande struck a cautionary note, warning that no individual leader should be allowed to stop closer European co-operation.
"It's the EU in question, not just one country in the EU," Hollande said as he arrived on Thursday.
"I want Britain to stay in the EU. But I hope most of all that Europe can advance, can be stronger."
Cameron is seeking changes to the UK-EU relationship that will let him urge Britons to vote "yes" to continued membership in a referendum that could come as early as June.
He told his fellow leaders that he needed a substantial deal that would be "credible for the British people".
The British referendum on EU membership is bound to be hard-fought, since few issues in Britain have as much resonance as its relationship with the EU.
"The question of Britain's place in Europe has been allowed to fester for too long," Cameron said, arguing that this was a chance to settle the issue for a generation.
Britain, which has one of the strongest economies in Europe, has been a magnet for hundreds of thousands of workers from EU nations in Eastern Europe seeking higher-paying jobs.
Britain has no power to stop immigration from other EU nations, leading some in Britain to say that immigrants are taking their jobs.
The EU immigrants can also claim unemployment, child care and other benefits in Britain, which the government claims is straining the country's social services budget.
Since none of the 27 other leaders has a desire to see Britain leave, there is broad consensus, if not agreement, on a deal which Cameron says he needs to win the referendum.
It would give Britain more powers to limit benefit payments to workers from other EU countries for several years - something Britain says will slow the pace of immigration.
The deal also offers guarantees to countries, including Britain, that do not use the shared euro currency, and makes tweaks aimed at boosting competitiveness and giving national parliaments more power.
But differences remain on key details, including Britain's wish to be exempted from the EU's longstanding aim of "ever closer union".
EU President Donald Tusk cautioned that a deal was not certain.
"This is a make-or-break summit, I have no doubts," he said.
The lingering disputes over everything from the reinforcement of national sovereignty to child benefits belie the fact that the other member states cherish Britain as an economic and diplomatic giant in a struggling EU.
"I'm going into this debate with the position that we would like to do everything to create the conditions so that Great Britain can remain part of the European Union," German Chancellor Angela Merkel said.
But continuing differences reveal an uneasy relationship.
Cameron argues for a "live and let live" union in which some countries move ever closer together while others remain semi-detached.
That grates against the wishes of France, Germany and others who believe strongly in an "ever closer union" among as many members as possible.
Britain has long been a half-hearted member of the EU, staying out of both the euro currency and the passport-free Schengen travel zone.
The perception of increasing Brussels meddling in affairs many Britons long considered sovereign issues made the time ripe for a referendum.
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