LONDON — Battered by serial defeats in Parliament, scolded by members of his own party, abandoned by even his own brother, Prime Minister Boris Johnson of Britain looked this week like someone who could use a friend.

He got one Thursday — or at least a faithful understudy — in the person of Vice President Mike Pence. Mr. Pence met Mr. Johnson at 10 Downing Street to pass along President Trump’s support of the prime minister’s plan to pull Britain out of the European Union.

Mr. Trump himself offered Mr. Johnson a long-distance pat on the back Wednesday as Mr. Johnson battled a recalcitrant Parliament, telling reporters, “Boris knows how to win.”

These days, however, Mr. Johnson does not look like much of a winner. He suffered back-to-back defeats in Parliament on his call for an election and his vow to withdraw from the European Union, with or without a deal, by Oct. 31. On Thursday, his own brother, Jo Johnson, resigned from Parliament and the government, saying he was “torn between family loyalty and the national interest.”