It was an abrupt turnabout, even for the easy-come, easy-go nature of alliances in Donald J. Trump’s political orbit.

For weeks, Elon Musk, Mr. Trump’s billionaire backer, had wrapped his arms around the British populist politician, Nigel Farage, promoting his insurgent, anti-immigrant party, Reform U.K., as the answer to the country’s problems.

But on Sunday, Mr. Musk posted, “The Reform Party needs a new leader. Farage doesn’t have what it takes.”

Mr. Musk did not explain his change of heart. But it appears linked to Mr. Farage’s refusal to endorse Mr. Musk’s demand that a far-right agitator, Tommy Robinson, be released from prison. Mr. Farage has distanced himself from Mr. Robinson, whose real name is Stephen Yaxley-Lennon and who has multiple criminal convictions in addition to a history of Islamophobic statements.

“Well, this is a surprise!” a studiously chipper Mr. Farage posted an hour after Mr. Musk. “Elon is a remarkable individual but on this I am afraid I disagree. My view remains that Tommy Robinson is not right for Reform and I never sell out my principles.”

Mr. Musk’s rupture with Mr. Farage was a new twist in the days-long barrage of increasingly strident, misinformation-filled posts about Britain from Mr. Musk, who appears intent on exercising the same influence in European countries that he did during the American presidential election.