Trump preceded his visit by urging Britain to walk away from the EU without an agreement.

President Donald Trump touted a "very, very substantial trade deal" between the United States and Britain after Brexit as he met Prime Minister Theresa May on Tuesday for fraught talks held amid street protests.

He joked to the outgoing British leader that she should "stick around" and reach a much stronger economic alliance with the United States once her country finally leaves the European Union.

"I think we will have a very, very substantial trade deal. It will be a very fair deal," he told her at a meeting with business leaders and ministers

"We're going to get it done."

Trump also ignored his past criticism of May's Brexit strategy and congratulated her on doing "a fantastic job" since taking office weeks after Britain voted in June 2016 to strike its own course after more than 40 years.

They spoke as thousands took to the streets of central London to protest everything from Trump's sceptical views on climate change to his embrace of anti-abortion groups.

Activists cheerfully inflated an orange blimp of a baby Trump dressed in a diaper outside parliament that brought morning rush hour traffic to a halt.

"Everything Trump stands for - misogyny, climate denying - everything about him is wrong," marble restorer Steve Gray told AFP.

"His climate denying is unbelievable, his foreign policy, everything about him," the 53-year-old said.

'Fantastic job'

The president's visit is technically centred around Wednesday's D-Day 75th anniversary commemorations on the south shore of England.

But it comes at an especially chaotic time for the UK.

May will step down as Conservative Party leader on Friday over her inability to deliver Brexit despite focusing on little else for the past two years.

She will stay on as prime minister until her successor is found among 12 contenders - one dropped out on Tuesday - who must make some tough choices before the twice-delayed Brexit deadline on October 31.

Trump preceded his visit by urging Britain to walk away from the EU without an agreement.

He also suggested that Brexit-backing former foreign minister Boris Johnson would be an "excellent" leader to get it done.

He appeared to try to make amends for his diplomatic faux pas on Tuesday.

"I'd just like to congratulate you on having done a fantastic job on behalf of the people of the United States and its an honour to have worked with you," Trump told May.

But the "special relationship" between the two sides is also being tested over different approaches to China and Iran.

Talks are likely to cover Britain's possible use of Chinese firm Huawei's technology in building its 5G network.

A senior UK government official told The Times newspaper that May would make "no apologies" over her reported decision to let Huawei build some non-essential parts of the next-generation mobile service.

The US administration has strongly hinted that this may limit its ability to share intelligence with Britain.

May told the business breakfast that Britain will strive to strike a "wider economic partnership" with its closest trading partner outside the EU.

"It is a great partnership, but I think it's a partnership that we can take even further," she said.

She gave Trump a copy of one of the most significant documents in the transatlantic "special relationship" - a framed copy of Winston Churchill's personal draft of the 1941 Atlantic Charter that which defined the Allied goals post-World War II.

The two also held a private tour of the Churchill War Rooms from which the prime minister ran his operations.

'Noise protests'

Their talks were accompanied by the sounds of "noise protests" of thousands of anti-Trump activists.

One group paraded a life-size doll of Trump - wearing his trademark red "Make America Great Again" cap - sitting on a toilet with a phone in his hands.

"It's hard to even know where to start with Trump," said Norwegian college student Helen Thuen.

"It's about the policies, that's what really matters. His personality affects his policies, though."

Trump's day will be rounded off with dinner at the US ambassador's residence.

The heir to the throne Prince Charles and his wife Camilla will attend on behalf of the queen.