Foreign policy analysts expressed astonishment that Mr. Trump would so cavalierly endanger that partnership. “It illustrates the extent to which the White House really doesn’t care what damage they do to crucial relationships in order to avoid admitting their dishonesty,” said Kori Schake, a former national security aide to President George W. Bush now at Stanford University’s Hoover Institution. “America’s allies are having to protect themselves against being tarred with the White House’s mendacity.”

Eric S. Edelman, an under secretary of defense under Mr. Bush, has written about the stresses between the United States and Britain in recent years. “I hope that this latest episode doesn’t drive a stake through the heart of the strongest remaining element of Anglo-American partnership,” he said.

Julianne Smith, who was a deputy national security adviser to Vice President Joseph R. Biden Jr., said Mr. Trump did not appear to realize how much American intelligence agencies depend on Britain in dealing with threats around the world. “He will probably live to see the day when he will regret firing off such an egregious insult to Britain and then failing to apologize for it,” she said…

“It’s very easy to have a good meeting with Trump,” said Jeremy Shapiro, a former State Department official who is the research director at the European Council on Foreign Relations in London. “He’s very pleasant in person. He’ll promise you the world. And 48 hours later, he’ll betray you without a thought. He won’t even know he’ll be betraying you.”