Addressing the 100-strong group the Prime Minister said there was an "unprecedented" opportunity to do a deal that boosted jobs and growth in both countries.
The plan has infuriated fervent Brexit supporters, who think it would limit Britain's ability to strike new trade deals around the world.
"There is no stronger alliance than that of our special relationship with the U.S. and there will be no alliance more important in the years ahead", May said ahead of the visit.
As Trump is expected to discuss a possible post-Brexit trade deal and other worldwide issues with May, organizers of Friday's demonstrations say there is no shortage of issues that will inspire mass numbers of people to attend.
"We in this country, and I hope I do not regret saying this, are very good at this sort of thing".
U.S. President Donald Trump escorts British Prime Minister Theresa May down the White House colonnade after their meeting at the White House in Washington, U.S., January 27, 2017. "But when they make you feel unwelcome, why would I stay there?" "I warned them. Immigration is taking over Europe". "What is interesting is Trump is not criticising mayors of those cities but he is criticising me", he said in an interview on the BBC Today programme.
Speaking about his visit to the United Kingdom at a press conference at the White House on Tuesday, Donald said that he is expecting to have an "interesting time in the UK", adding: "So I have North Atlantic Treaty Organisation, I have the United Kingdom - that's a situation with turmoil, and I have Putin". I think he is a great representative for your country.
"I am not pitting one against the other", the United States president said when asked if he'd like to see Johnson as PM.
The president says "Brexit is Brexit", and suggests the prime minister is moving away from that. "I think that's why Brexit happened".
Melania and Donald Trump disembark Air Force One at Stansted Airport, north of Londo. 'You go through certain areas that didn't exist ten or 15 years ago.' He added: 'Allowing the immigration to take place in Europe is a shame'.
The state visit has never been scheduled - there is fierce opposition to it in many quarters of Britain - and this trip is part of a working visit instead, meaning, among other things, that Trump will overnight at Winfield House, the USA ambassador's handsome residence near Regents Park rather than in Buckingham Palace or Windsor Castle as a guest of the queen.
Some carried placards saying Special Relationship?
Trump's intervention comes at the end of a tumultuous few days for May.
They were given a best-of-British dinner, featuring Scottish salmon, Hereford beef fillet and strawberries with clotted cream ice-cream.
In a near replay of their famous hand-holding at the White House, the president briefly took Mrs May's hand after arriving as they went up the stairs into the palace following a performance from a military band.
On Thursday night, hundreds of demonstrators chanted outside the US ambassador's residence where Trump was staying on the outskirts of London, providing a preview of the forceful protests expected on Friday.
Marcus Fysh, MP for Yeovil, has accused people inside government of "lying to MPs faces about what they are doing", after writing a piece for Brexit Central.