Mr. Kerry, usually the optimist, sounded almost downbeat as he arrived in Italy. He did not make any references to a “shriveled Europe,” as one of his top aides did in a conversation over the weekend. But he made clear that European allies are also going to have to rethink their relationships with the United States.

“Twenty-two of the nations in the E.U. are members of NATO,” he said less than a minute into his meeting with his Italian counterpart, Paolo Gentiloni. He warned that the most critical step was to “work together to provide as much continuity, as much stability, as much certainty as possible” to “protect the values and interests that we share in common.”

The problem is that no one shares those values and interests quite the way the British do, a belief that no American diplomat would utter in public for fear of offending other members of the European Union. But British officials who have been at the center of that daily interaction say the concern goes both ways.

“I worry that we will have less clout on our own: In the future we won’t have as much influence on Europe’s response to Putin’s transgressions, Iran’s nuclear ambitions, or the E.U.’s foreign and security policy,” said Peter Westmacott, one of Britain’s most experienced diplomats and, until January, ambassador to the United States. “And we will be less able to ensure it is U.S.-friendly.”

He added that without Britain’s direct involvement, Europe was likely to be less enthusiastic about free trade.

Still, Mr. Westmacott noted that “we should be able to cooperate much as in the past on counterterrorism, on intelligence, on cyber and on military issues,” assuming that “our economy does not shrink too much as markets, investors and the Scots take stock of Thursday’s outcome.”

All of which raises the question: If Britain can no longer play that indispensable role for Washington, surely there is another country that can? Perhaps, but it is hard to think of who.