LONDON — Britain has long been anxious about its “special relationship” with the United States, but after some choice remarks about Donald J. Trump by members of the governing Conservative Party during the presidential campaign, the relationship needs a bit of nurturing. And who better to tend to that, in his own mind at least, than Nigel Farage, the beer-loving commodities-trader-turned-populist-leader of the U.K. Independence Party.

Mr. Farage, known for his noisy role in promoting Britain’s exit from the European Union, was the first foreign politician to meet with President-elect Trump, three months after joining him on the campaign trail. On Monday, a photograph of the two men inside Trump Tower, all grins and thumbs up, dominated the front pages of newspapers in Britain.

As some in Mr. Farage’s party suggested him as the next ambassador to the United States, Prime Minister Theresa May’s office on Monday was quick to slap him down, saying that there would be no “third person” in her relationship with Mr. Trump.

Responding to the cool reception from the prime minister’s office, Mr. Farage told LBC Radio: “ It just goes to show they are not really interested in the country or the national interest, they are more concerned about petty party politics and trying to keep me out of everything.”