May's official spokesperson said the UK government already has "well-established" channels of communication with Trump's team, dismissing the need to seek help from far-right UK Independence Party (UKIP) leader Nigel Farage.
"The president-elect talked about enjoying the same relationship as Thatcher andReagan. I don't recall there being any third person in that relationship," the spokesperson told reporters.
Downing Street sharply dismissed suggestions that Farage could help to broker a relationship between May and Trump due to his closeness to the new president.
The comments came as UK foreign secretary Boris Johnson also sought to downplay any concerns over US-UK relations under a Trump presidency.
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Speaking to reporters as he arrived in Brussels for a meeting with counterparts, he said, "I think there's a lot to be positive about. It's very important not to prejudge the president-elect or his administration.
"It's only a few days since the election has taken place. I think we all need to wait and see what they come up with but I think we should regard it as a moment of opportunity," he said.
In December, Johnson said Trump was "clearly out of his mind" if he thought the Muslim ban was a good idea, accusing him of "playing the game of the terrorists and those who seek to divide us".
He had also attacked Trump for suggesting police were afraid to visit some parts of London because of radicalisation, saying "I think he's betraying a quite stupefying ignorance that makes him frankly unfit to hold the office of President of the United States" adding "the only reason I wouldn't go to some parts of New York is the real risk of meeting Donald Trump".
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