LONDON – President-elect Donald Trump has suggested in a tweet that British Prime Minister Theresa May should make Nigel Farage, who played a key role in Britain’s vote to leave the European Union, her government’s ambassador to the United States.

The suggestion appeared to take the elected leaders of his country by surprise, and British Prime Minister Theresa May’s office quickly made it clear he would not be given the job.

It is the role of each country to name its overseas representatives, and public recommendations from host nations are uncommon.

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The unusual call from Mr. Trump clearly showed the scale of his liking for Farage, who played a key role shaping public opinion in favor of taking Britain out of the EU ahead of the June referendum.

Many people would like to see @Nigel_Farage represent Great Britain as their Ambassador to the United States. He would do a great job! — Donald J. Trump (@realDonaldTrump) November 22, 2016

Mr. Trump tweeted late Monday night that “many people” would like to see Farage head Britain’s U.S. mission, adding: “He would do a great job!”

Mr. Trump’s tweet received a cool response in official circles. A spokesman for May said there was “ m,no vacancy for an ambassador to the United States,” and added the current envoy was doing a fine job.

May had earlier rejected the notion that Farage could serve in an unofficial role as liaison to Trump.

Speaking Tuesday morning to CBS News partner network Sky News, Farage said he was “flattered” by the suggestion.

Asked about remarks he made just last week, in which he said: “I don’t think I’m the ambassadorial type... I am not sure diplomacy is necessarily at the top of my list of skills,” Farage changed his tune, suggesting, “the world has changed.”

“I would like to play a positive role in relations between our two countries,” he added in the Tuesday interview with Sky News.

Farage said in a lengthy article published on the Breitbart news website -- just four hours after Mr. Trump’s tweet -- that the president-elect’s suggestion of an ambassadorship had hit him “like a bolt from the blue,” but he went on to say it was representative of the sense of loyalty he understood Mr. Trump to hold dear.

“Nothing could have prepared me though for what came next. Like a bolt from the blue Trump tweeted out that I would do a great job as the UK’s Ambassador to Washington. I can still scarcely believe that he did that though speaking to a couple of his long time friends perhaps I am a little less surprised,” wrote Farage. “They all say the same thing: that Trump is a very loyal man and supports those that stand by him.”

It was a great honour to spend time with @realDonaldTrump. He was relaxed and full of good ideas. I'm confident he will be a good President. pic.twitter.com/kx8cGRHYPQ — Nigel Farage (@Nigel_Farage) November 12, 2016

Farage’s cozy relationship with Mr. Trump developed during the presidential campaign, when hebriefly appeared with the Republican nominee, and he was the first foreign politician to meet with Mr. Trump after the election.

The two were photographed smiling broadly outside a golden elevator at Trump Tower in Manhattan.

Mr. Trump’s overture to Farage, who has failed to ever win a seat in Britain’s Parliament but who has represented the U.K. in the European Parliament for years, while fighting to remove it, was the focus of a question and answer session for the nation’s to diplomat on the floor of the Parliament later Tuesday morning.

Lawmakers from Foreign Minister Boris Johnson’s own Conservative Party and the Labour opposition made it clear they didn’t appreciate an incoming American leader weighing in so directly on matters of British domestic politics.

British Foreign Secretary Boris Johnson gestures during his visit to the Foreign Ministry, Nov. 4, 2016 in Berlin, Germany. Getty

Conservative MP Simon Burns jokingly suggested that Johnson might return the favor and offer some advice of his own to the Trump administration; that they pick Hillary Clinton as ambassador to the U.K.

In the British media, Mr. Trump’s tweet was portrayed as a thinly veiled jab at the British political leaders (including Prime Minister May and Foreign Minister Johnson) who had stood in opposition to Farage’s Brexit campaign, and at British politicians (again, including Johnson) who were critical of the Republican billionaire during his campaign.

Farage seized upon the theme himself in his Breitbart article:

“The political revolution of 2016 now sees a new order in charge of Washington. In the United Kingdom the people have spoken but the players at the top have, I am afraid, stayed the same,” wrote Mr. Trump. “Those who supported Remain now hold senior positions. Worst still, those who were openly abusive about Trump now pretend to be his friend.”

Confronted by a Labour MP about whether he would insist in their meetings that Mr. Trump keep up current U.S. commitments to combat climate change, Johnson said it would be unfair to judge the new president based on campaign trail rhetoric, and insisted he was waiting to see what policy actually comes from the White House.

British officials have said the government is considering inviting Mr. Trump to make a state visit after he assumes the presidency.