The president, who has said Boris Johnson would be an "excellent" leader, said the Government has to "get the deal closed".
US Ambassador to Britain Woody Johnson told BBC television that Washington was already preparing the way for a trade deal and it would be done "as expeditiously as any agreement we've ever had".
"We have got to have the courage to tell the people of this country we can do it, if we want to", he told one voter on the doorstep.
Trump also suggested that his friend Nigel Farage-the divisive leader of the right-wing Brexit Party, which was the biggest victor in the U.K.'s European Parliament elections last month-should be involved in negotiations with the EU.
"Think how well they would do if they did", he added.
On the Brexit divorce bill, Trump said: "If I were them, I wouldn't pay 50 billion dollars".
He said he would expect Britain to be open to U.S. agricultural products, and when asked about access of USA firms to Britain's cherished state-run health service, said "all things that are traded would be on the table".
Opposition leaders Jeremy Corbyn and Vince Cable have both boycotted the dinner in protest at Trump.
Mr Trump's arrival in the capital is due to be followed by a protest through central London against the visit on Tuesday, with the Trump Baby blimp made for his visit a year ago due to put in an appearance.
Mr Nancarrow, who runs an online eco-marketplace, told the Bishop's Stortford Independent: "Donald Trump and his denial of climate change are not welcome and I want him to be fully aware of that when he flies into Stansted".
Bolton dismissed concerns about Brexit: "You know, America declared its independence once - we made out okay", he quipped. A deal at any price was their logic. He knows what he is talking about.
Leadership rival Jeremy Hunt, one of the staunchest opponents of no deal, told the BBC that it should only be used "in extremis" but that he believed he could negotiate a better deal before October 31 - the country's current exit date.
Other Conservative lawmakers in the leadership race had sought his backing, he said, although not environment minister Michael Gove, who has criticized his stance on Iran.
He said: "I wanted to protest to Trump about his denial of climate change". "Dark clouds are forming once again in Europe, and rather than encourage those forces we need to find much better tools to defeat them". "It's actually about the future of the entire western world".
"That means leaving the European Union, irrespective of whether it's on their terms or not, with no deal".
Trump said instead of demonstrations, there had been "tremendous crowds of well-wishers". "If they don't accept that we should leave on world trade terms".
Britain is hoping Trump's visit will bolster its ambitions to work out a free trade deal with the United States if Brexit means a go-it-alone trade policy.
Ajuub Faraji, a Trump blimp "babysitter", said: "Trump is a risky, divisive demagogue and we're thrilled that the public have put their hands in their pockets to support groups fighting the impacts of his policies".
Mr Trump has already made headlines before his visit by wading into two political issues in the United Kingdom: the country's future prime minister and Brexit. She is in her final days as Tory leader, although she remains PM. After being greeted by the queen and heir-to-the-throne Prince Charles at Buckingham Palace, he will enjoy lunch with the 93-year-old monarch and other senior royals.
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