"As the U.K. makes preparations to exit the European Union, the United States is committed to a phenomenal trade deal between the US and the U.K.", Trump said Tuesday in London during a news conference with British Prime Minister Theresa May.
He also joked about who might be a suitable successor in Downing Street.
President Donald Trump promised the USA and United Kingdom could as much as triple their trade after Brexit, but stirred controversy by hinting that Britain's government-run health system could be opened to American companies.
May will make clear to Trump that Britain is reviewing "the right policy" on Chinese company Huawei and its involvement in the UK's 5G telecommunications network, the spokeswoman added.
"We will want to see better access to services in the U.S. and we will have to offer something in return", Fox told BBC radio on Tuesday. "This is not a Burger King buffet at Mar-a-Lago", the Queen told Trump in the clip.
But despite warm exchanges with British royalty, Trump has already ruffled feathers with controversial comments about the mayor of London.
Some of Britain's largest-ever demonstrations against a foreign leader were also taking place on Tuesday.
The protesters are following Trump wherever he goes in London and have vowed to bring the central part of the city to standstill.
"We're trying to remind the president how unwelcome he is in this country", said Leo Murray, 42, the co-creator of the six-metre-high blimp. She also declined to chastise Trump for any of the remarks he made about the two politicians. "We want to put a smile on people's faces as well as make a serious point".
As for Jeremy Corbyn, the president said he had refused a request to meet the Labour leader, dismissing him as "a negative force", clearly believing this is not a man he is likely to have to work with any time soon.
The president's three-day visit is centred around Wednesday's D-Day 75th anniversary commemorations on the south coast of England, after which he will visit Ireland and Normandy, northern France. Before his touchdown at Standstead airport, Trump tweeted the mayor was a "stone cold loser".
A "Resist Trump" banner from Amnesty International hangs from the Vauxhall Bridge following Trump's arrival in the UK.
Trump preceded his visit by urging Britain to walk away from the European Union without an agreement. Shakira Rahman, 11, joined a group of other demonstrators outside Buckingham Palace ahead of Monday's banquet.
At Buckingham Palace, Melania - in an elegant, white below-the-knee Dolce & Gabbana dress with navy blue collar and belt and a custom hat by Herve Pierre - stood alongside the queen and Charles's wife Camilla, while Charles and the president inspected the guard.
Up to 250,000 people were expected to show up for the march against Trump's state visit from Trafalgar Square to the Houses of Parliament.
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