LONDON — When the European Union unexpectedly won the Nobel Peace Prize last week, the leaders of Germany, France and Italy spoke of their pride. The British prime minister, David Cameron, who will join those leaders at an E.U. summit meeting in Brussels on Thursday, maintained an awkward silence.

In Britain these days, even peace is controversial if associated with the Union.

On Monday, the British government said it wanted to opt out of an estimated 133 E.U. police and judicial cooperation measures to which it had once agreed.

A week earlier, Mr. Cameron supported a plan for a new budget for countries that use the euro, something that would place his country, which does not use the euro, firmly in Europe’s outer tier. The prime minister has been hinting he could hold a referendum on Britain’s relations with the Union, and one newspaper reported Sunday, to no denial, that a senior cabinet minister wanted Britain to threaten openly to leave the 27-country bloc.

All of this has fueled concerns that Britain is moving inexorably toward the E.U. exit door. Political and financial pundits have coined a term for this development: “Brixit,” a variant on “Grexit,” the shorthand for Greece’s much-predicted departure from the euro zone.