He also agreed to work for a seamless transition to a new bilateral relationship as soon as Britain leaves the Brussels bloc.
The first step will be a new Trade Negotiation Agreement (TNA) that will see high-level talks between the two nations beginning immediately.
Theresa May and Donald Trump will work out trade deals between the UK and US
This will pave the way for a new UK/US trade agreement to be ready as soon as possible post-Brexit.
Mrs May is understood to have discussed the urgency of the matter with Congress Speaker Paul Ryan in Philadelphia on Thursday.
He is also wants early negotiations.
May meets Trump: Historic first meeting in pictures
Fri, January 27, 2017
The two leaders will spend about an hour in face-to-face talks in the Oval Office, where President Trump has restored a bust of Winston Churchill removed by predecessor Barack Obama.
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President Trump Meets With British PM Theresa May At The White House
The news comes just days after the British Government was warned that trade talks with countries outside the EU could break the law and significantly undermine its efforts to negotiate a favourable Brexit deal.
I’m pleased to have agreed a shared ambition with President Trump for a Trade Negotiation Agreement
One London-based European diplomat said: “They do need to be careful about this. No one will object to broad preliminary talks, but anything that looks like proper negotiations… that would certainly not be well received.”
The discussions are expected to be led by the International Trade Secretary Liam Fox and his US counterpart Wilbur Ross, who sparked controversy by claiming Brexit was a “God-given opportunity” for other nations to take business away from the UK.
Any trade deal between the two nations would be still illegal under EU law
Mrs May said: “I’m pleased to have agreed a shared ambition with President Trump for a Trade Negotiation Agreement that will benefit both our countries.
“It’s a step forward that underlines our commitment to use the opportunities of Brexit to build a truly global Britain.
“This is the first step leading to a future trade deal with the US which could provide huge benefits to our economic muscle and will give businesses additional certainty and confidence.”
The first round of talks with the US president ended positively
Trump has indicated he wants to broker a deal within 90 days and is said to have questioned why the UK must wait until it leaves the EU before reaching a new agreement with the US.
An insider said: “He wants to get on with things as fast as possible – already the hallmark of his first 10 days in office. His view is that the UK has voted to leave.
“What can the EU do to the UK that could stop it from beginning on its path to independence?”