The British prime minister holds high-stakes talks before a crucial referendum on whether to abandon European integration. Though distracted by other problems, the German chancellor tries to help him out. Back home, British critics snipe, hoping the negotiations will collapse.

That is broadly the position faced by Prime Minister David Cameron of Britain this week as he enters delicate discussions over his country’s membership terms in the European Union, ahead of a plebiscite on whether to quit the bloc.

But it was also the situation more than four decades ago, when Britons last had the opportunity to vote on their European destiny. And pro-Europeans are hoping that history will repeat itself.

Under pressure from critics of European integration within his Conservative Party, Mr. Cameron has promised to hold a referendum by the end of 2017, and at a summit meeting in Brussels on Thursday he will press for a “better deal” from partners on the Continent.

At stake is not just Britain’s membership in the 28-nation bloc, but also perhaps the future of European integration, because the union can ill afford the shock that a British exit would bring.