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The Prime Minister said she hopes to hold “very frank” talks with the president when she visits Washington DC.

Some reports speculated that May will travel to see Trump as early as next week, but No. 10 has made moves to quash the rumours.

May's confidence is another move suggesting post-Brexit Britain can make strives with international trade.

And it comes in spite of Mr Trump’s assertion of an “America first” plan that initially sparked concerns that a quick deal would be difficult.

(Image: REUTERS)

Many hoped that a new US-Britain trade deal would offset any Brexit-related economic hit.

The president promised that "every decision on trade... will be made to benefit American workers and American families".

And Mrs May said in an interview with the Financial Times: "I'm confident we can look at areas even in advance of being able to sign a formal trade deal.

"Perhaps we could look at barriers to trade at the moment and remove some of those barriers to open up that new trading relationship."

Foreign Secretary Boris Johnson backed the PM saying he was "very optimistic" about striking a strong trade deal.

He said while visiting Burma: "I think that the new president has made it very clear that he wants to put Britain at the front of the line for a new trade deal and obviously that's extremely exciting and important."

(Image: REUTERS)

But concern has also been raised over Mr Trump’s commitment to scale back US involvement with NATO, which has sparked fears of increased Russian aggression.

President Putin has already said he is ready to meet Trump in the coming months, and they are expected to discuss NATO and US sanctions.

Trump complained that the US had spread its armies into other countries to defend their borders while refusing to “defend our own”.

But Mrs May said: "I'm also confident the USA will recognise the importance of the co-operation we have in Europe to ensure our collective defence and collective security."

(Image: GETTY)

While suggesting a “very special relationship” between the UK and the US was achievable, the PM refused to compare it to the Reagan-Thatcher-style relationship of the 1980s.

She said she does not want to “emulate” past models, and also made it clear she found Trump’s comments about women “unacceptable”.

Meanwhile protests continue around the world against President Trump taking office.

Women’s marches are being held in a number of countries as thousands line the streets in Washington DC near the White House.