The Prime Minister held talks with Donald Trump in New York and the pair spoke on friendly terms as they discussed hopes for a deal.
Mrs May also gave a speech at the United Nations where she tried to reassure those who fear that Britain will become more isolationist after Brexit.
She said: ‘The vote by the people to leave the EU was not a rejection of multilateralism or international co-operation.
‘It was a clear demand for decisions and accountability to lie closer to home.
‘I believe the role of leadership in these circumstances is clear – it is delivering on the democratic wishes of our people and international co-operation, working with allies and partners in pursuit of our shared values.’
Praising the Prime Minister’s handling of Brexit, President Trump told reporters: ‘She’s working very hard, like all us, and doing a very, very good job…
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‘I will say that we are talking about a lot of different things today, trade, military, security, protection all sorts of things.
‘We have a myriad of things to talk about.’
The PM and President began their meeting by ‘discussing their mutual desire to form a wide-ranging trade deal’, a No 10 spokesman said.
‘They agreed that Brexit provides a wonderful opportunity to strike a big and ambitious UK-US Free Trade Agreement.’
Ahead of the meeting, Mrs May was asked how she could persuade a sceptical British audience to trust the President and pointed to his action on the Salisbury spy poisoning and his change of heart on the Nato alliance.
She added: ‘In relation to a trade deal in the future I would say President Trump and America want to do a good trade deal with us.
‘It’s in both our interests to do that good trade deal.’
Despite the positive tone of the meeting with Trump, business leaders in New York laid bare their fears over Brexit to Mrs May, and said they believe it could lead to the fall of her government.
During a question and answer session after her speech to the UN, Steve Schwarzman, chief executive officer at investment firm Blackstone, said the UK’s exit from the EU was ‘daunting’.
He told the PM ‘things could really go off with a bad Brexit’ and called for reassurances for the business community.
Mrs May acknowledged there was ‘uncertainty’ about Brexit and admitted ‘we don’t know when the negotiations will end’.
But she added that she believed the UK would secure a good deal in the negotiations with the European Union.