British Prime Minister Theresa May (2nd from left) and her husband Philip John May(left) pose with US President Donald Trump and US First Lady Melania Trump outside 10 Downing Street in London on Tuesday on the second day of their three-day state visit to the UK. Photo: AFP

US President Donald Trump touted a "very, very substantial trade deal" between the US and Britain after Brexit as he met Prime Minister Theresa May on Tuesday for 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 US 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, adding: "We're going to get it done."

Despite having repeatedly criticized May's Brexit strategy, Trump said she had done "a fantastic job."

Nearby, left-wing activists inflated an orange blimp of a baby Trump dressed in a diaper at a rally outside parliament that brought morning rush hour traffic to a halt.

It signaled the start of what are expected to be large protests against the president on the second day of his three-day state visit.

"Trump baby is just a mascot for a massive movement against Trump's hateful and divisive politics," organizer Leo Murray told AFP. May will step down as Conservative Party leader on Friday over her inability to deliver Brexit despite focusing on little else in almost three years in office.

She will stay on as prime minister until her successor is found among 13 contenders who must make some difficult choices before the twice-delayed Brexit deadline on October 31.

Before he arrived, Trump urged 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 it's an honor 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.