Boris Johnson has held talks with senior members of Donald Trump's team during a surprise visit to NY.
May had told Sky News earlier in the day that she was sure that Britain and the United States would build on their close ties and that their "special relationship" would endure despite describing some of his comments about women as "unacceptable".
The Foreign Secretary was expected to meet Mr Trump's son-in-law Jared Kushner and the president-elect's strategist Steve Bannon in NY. Today, Johnson will meet Congressional leaders in Washington, including Speaker Paul Ryan, Senator Bob Corker and Senator Mitch McConnell.
Johnson, a former mayor of London, became the principle diplomat for Great Britain following the narrow success of 2016's referendum to leave the European Union, commonly referred to as Brexit.
Mr Johnson's visit followed talks between the Trump camp and Mrs May's closest advisers Nick Timothy and Fiona Hill.
The sessions involved Trump's chief strategist, Steve Bannon, and the president-elect's son-in-law, Jared Kushner, on Sunday evening before Johnson traveled to Washington to visit with congressional leaders.
"It's based on shared values and it is a relationship where, actually in the United Kingdom, we feel we can say to the U.S. if we disagree with something that they are doing".
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Mr Johnson said then: "The only reason I wouldn't go to some parts of NY is the real risk of meeting Donald Trump".
The Prime Minister and Mr Trump are due to meet in Washington within weeks of his inauguration on January 20.
The status of the special relationship between the two long-time allies has faced fierce speculation ever since Mr Trump won the USA presidential election.
Johnson's visit comes hours after Trump tweeted he is "very much" looking forward to meeting Prime Minister Theresa May in the spring, and described the United Kingdom as a "very special" ally.
Downing Street has repeatedly dismissed Farage's offer to help her build a relationship with Trump's administration.
Trump said he is "looking forward" to meeting May. In the run-up to the November 8 U.S. presidential elections, the British Foreign Secretary had defended Trump from criticism in Europe.
Last month, she took the unusual step of issuing a statement distancing Britain from a speech made by outgoing US Secretary of State John Kerry about Israel in a move seen as a bid to please the Trump team. "We will be able to have control of our borders, control of our laws", May said.