Britain’s departure “changes the balance within the E.U. and creates a power vacuum,” said Mark Leonard, the director of the European Council on Foreign Relations. “The absence of Britain will make the relationship between France and Germany even more toxic,” he said.

“But it also destabilizes a lot of the countries, like the Dutch and the Nordics, on issues like the free market, anti-Russia policy and trans-Atlanticism,” Mr. Leonard added. “And it will further the imbalance between the eurozone and non-eurozone countries, leaving those like Poland, Sweden and Denmark more exposed.’’

Central European countries, Turkey and countries hoping to join the bloc may also feel Britain’s absence.

“The Turks are quite concerned, because Britain has been a friend in terms of Turkish integration, even if accession is not on the cards,” Mr. Lesser said.

The European Council, made up of European governments, has already approved the deal, but will make a final, pro forma vote in writing on Thursday.

Britain’s economy is roughly the size of France’s, the second-largest in the European Union, and is an important security player, a nuclear power with a permanent seat on the United Nations Security Council. Britain has a close relationship with Washington and, even after its famous rebate, is the second-largest net contributor to the bloc’s budget, putting in nearly 12 percent.

Already, as European governments debate the next seven-year budget — always a sour process — there are angry disagreements on how large it should be, given the need to fill the hole the British will leave behind when the transition period ends in December.