Theresa May’s historic visit to America was mired in controversy tonight as Donald Trump’s presidency was rocked by a wave of fresh scandals.

As the Prime Minister touched down in Philadelphia she indicated that the UK could stop sharing intelligence with the CIA after Mr Trump gave his backing to waterboarding in tackling Isis.

Asked about British rules stating that British spies cannot work with nations that use torture, Ms May said: “We condemn torture and my view on that won't change – whether I’m talking to you or talking to the President.”

Her rebuke to Mr Trump came as his fledgling presidency was hit by a series of new controversies, including:

The Mexican President, Enrique Peña Nieto, cancelled a meeting with Mr Trump in Washington next week a day after Mr Trump unveiled his plan to build a wall between the US and Mexico

Human rights groups expressed alarm over Mr Trump’s decision to publish a weekly list of crimes committed by immigrants in the US, saying the “shocking” and “xenophobic” move will “terrorise communities across the US”.

The entire senior level of management officials at the US State Department resigned – hours after a visit from new incoming Secretary of State Rex Tillerson

The President was due to sign an executive order launching an investigation into voter fraud during the US election, despite Republican House Speaker Paul Ryan saying he had seen “no evidence” of problems

Despite the issues facing Mr Trump, Ms May said she believed she could forge a close relationship with the President, declaring: “Haven’t you ever noticed? Sometimes opposites attract.”

She made the statement as she flew to meet Mr Trump and just days after thousands of women marched across the world in solidarity against the President and his sexist comments.

Anti-Trump protesters in Philadelphia on Wednesday (EPA)

As the Prime Minister left Heathrow today, on her way to becoming the first foreign leader to meet the new President, it was unclear how well the more reserved vicar’s daughter would gel with the most outlandish leader ever to sit in the Oval Office.

However, the Prime Minister said the most important thing about her trip was that she would “be able to sit down with President Trump and talk to him face to face about the issues, about the interests that we share”.

She added: “I’m sure that I will leave with a very clear picture. I want to give him a very clear picture of the UK.

“But also I believe that what will come out of this is a very clear determination on both sides not just to maintain the special relationship but to build the special relationship for the future. I think there is a real role for the UK and for the US working together.”

Ms May tonight visited a congressional Republican Retreat, where she gave a speech with a particular focus on foreign policy. Tomorrow she will meet Mr Trump at the White House for crunch trade talks and the opportunity for a photocall that will help set the tone for the relationship between Ms May and the President.

However, hopes for a smooth start to the landmark visit were dealt a blow after Mr Trump expressed his support for torture when interrogating terrorist suspects, saying that the US had to “fight fire with fire”.

Trump boards Air Force One for first official flight as President

The Prime Minister was asked about British guidelines stating the country’s spies cannot work with other nations’ agencies that practise torture.

Speaking as she flew to the United States, she said the UK’s guidance is “very clear” and that the approach towards torture had not changed and would not.

After being repeatedly pressed on the UK position of not sharing intelligence with countries practising torture, she said: “Our guidance is very clear about the position that the UK takes, and our position has not changed.”

She added: “The real question you should be asking is what do we think about torture? What we think about torture is we condemn it. We do not believe in torture. That position has been clear for some time and that position is not going to change.”

Mr Trump is expected to rip up restrictions put into place by Barack Obama after earlier stating that he wanted to bring back waterboarding and a “hell of a lot worse”.

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Ms May was on Wednesday challenged over the issue in the House of Commons by Tory MP Andrew Tyrie, who demanded the UK not be “dragged into facilitating” torture.

In a further controversial move, the Prime Minister left the door open for the greater involvement of US corporations in the NHS as part of a future trade deal.

Ms May would say only that she was committed to a health service that was free at the point of delivery, but made no comment on whether the NHS would be off the table in any future talks.

Asked whether health services might form a part of a potential deal, she said: “We're at the start of the process of talking about a trade deal. We're both very clear that we want a trade deal.

Ms May spoke in Philadelphia (AP)

“It will be in the interests of the UK from my point of view, that's what I'm going to be taking into the trade discussions that take place in due course. Obviously he will have the interests of the US. I believe we can come to an agreement that is in the interests of both.”

Asked again whether the NHS would be off the table, she said: “As regards the NHS, we're very clear as a Government that we're committed to an NHS that is free at the point of use.”

The statement left open the possibility of the greater involvement of US firms in healthcare, as long as people do not have to pay for the services they provide at the moment they are received.

One of the key factors that led to opposition to the TTIP trade deal between the US and EU was fear over whether it would open up the NHS to vast multinational corporations that might put the profits ahead of patient care.