German Chancellor Angela Merkel arrives at the European Union headquarters in Brussels. (Stephane De Sakutin/AFP/Getty Images)

E.U. leaders gathered Wednesday without Britain for the first time in four decades for a painful inward look at a union challenged as never before, with stark divisions remaining about how to avoid a further crackup.

E.U. leaders appeared united a day earlier in taking a hard line against British desires to pick and choose the best parts of membership as they look ahead to talks over Britain’s break. But disagreements remain about how far to cast the island nation into exile.

There is even less consensus about how to salvage the rest of the union.

Some leaders want to bind themselves together even more tightly in a bid to fend off Euroskeptic forces that might want to copy last week’s British referendum on E.U. ties. Others say the only way to survive is by loosening the confederation and scaling back E.U. ambitions. 

For now, mindful of the risks of ballot-box rebellions, many agreed on one tactic: avoiding more referendums in the 27 countries still in the E.U. fold. In a June 23 plebiscite, 52 percent of British voters chose to leave the European Union after a divisive campaign.

“We can see that a referendum in one country can have so much impact on everyone,” said French President François Hollande, who is facing a rabble-rousing anti-E.U. challenge ahead of elections next year. “You cannot just organize a referendum for your own purposes.”

E.U. leaders recognize that Britain may not be the only nation where the electorate is far more Euroskeptic than those in charge. Sentiments in Greece, France and Spain show many are wary of the European Union, according to a poll this month from the Pew Research Center.

Even E.U. stalwart Germany is nearly split down the middle, with 48 percent disapproving of the union. And anti-E.U. parties are flourishing from Finland to Austria to Italy.

“We all need to wake up and smell the coffee,” Lithuanian President Dalia Grybauskaite said as she entered a breakfast meeting of the 27 leaders.

Amid the disagreements, however, there was unity that Britain cannot have it both ways: wriggling loose from requirements on open borders with the rest of Europe while keeping access to Europe’s vast consumer market, the largest in the world. That has been the hope of the British “leave” campaigners, although there appeared to be a growing realization in London that they may be outgunned on the question.

“Access to the single market requires acceptance of all four freedoms, including the freedom of movement. There will be no single market a la carte,” said European Council President Donald Tusk.

In one measure of expectations for the outcome of the negotiations, French and German banks are increasingly looking at the market turmoil as a golden business opportunity. They are salivating at the possibility that the financial hub of London may dwindle in favor of Paris and Frankfurt, if Britain loses access to the E.U.’s banking market. 

In an appearance in Britain’s House of Commons on Wednesday, Prime Minister David Cameron seemed to acknowledge that his successor will be hard-pressed to win any meaningful concessions on immigration if the country wants to maintain single-market access. 

Asked by former defense secretary Liam Fox, a fervent Brexit campaigner, whether retaining the E.U.’s free-movement rules would be a “betrayal of millions of people who voted to leave,” Cameron said it was “difficult” to try to change the free-movement rules from within the E.U. and will be “even more difficult from outside.” 

Cameron had sought agreement in February from fellow E.U. leaders to allow national governments greater control over who can resettle in their countries. But he was largely rebuffed, leaving him with little to show for the negotiation and vulnerable to charges from the “leave” camp that Britain would never bring down record immigration levels while it remained in the E.U.

German Chancellor Angela Merkel, who has lost a rival power base with the British exit, said E.U. leaders had a “profound discussion” about what they need to do to keep the European Union from further fracturing.

“The union needs to give prosperity and security to its people,” she said after Wednesday’s meeting. “It’s not about more or less Europe, but that we have to be better in achieving the results in the objectives that we set out.”

E.U. leaders plan to meet again in September in Bratislava, Slovakia, to further discuss strategies to hold Europe together.

Underlining the quick-shifting realignments unleashed by the British vote, Scottish First Minister Nicola Sturgeon was also in Brussels as the leaders met, seeking an arrangement separate from any with the rest of Britain.

Scotland voted heavily to remain within the European Union, and Sturgeon has vowed that it will stay connected to Europe — even if that means a rerun of a 2014 secession vote in which Scotland opted not to leave the United Kingdom.

Sturgeon met with the heads of two E.U. institutions, European Parliament President Martin Schulz and European Commission President Jean-Claude Juncker. Other leaders declined her request for meetings, in part because E.U. member Spain is fearful of encouraging its own separatist regions to break away.

Griff Witte in London contributed to this report.