U.S. President Donald Trump (L) and British Prime Minister Theresa May leave 10 Downing Street in London, Britain, June 4, 2019. (Xinhua/Ray Tang)

LONDON, June 4 (Xinhua) -- British Prime Minister Theresa May said Tuesday that she and U.S. President Donald Trump wanted an ambitious trade agreement after Brexit.

May made the remarks at a joint press conference after the talks with Trump.

Trump said he believes Britain can have a "very very substantial trade deal" with the U.S. after it leaves the European Union (EU).

"I think everything is on the table... NHS (National Health Service) or anything else," he said, responding to a question on whether everything would be on the table in the talks on a trade deal between the two countries.

Woody Johnson, U.S. ambassador to the UK, has suggested the NHS should be "on the table" of a trade deal with the U.S. on a recent talk show.

He said in the BBC program that U.S. companies in the private sector should be able to bid for contracts in this public sector.

The U.S. President was greeted with a royal family welcome and protests after he arrived in London on Monday for a three-day state visit. Protestors were out in force across the capital, mainly outside Buckingham Palace and the heavily fortified U.S. ambassador's official residence in Regent's Park.

Trump held talks with May on Tuesday morning and would attend a D-Day commemoration during the visit.