Video report by ITV News Political Editor Robert Peston
Donald Trump has revealed he turned down a meeting with Jeremy Corbyn, as he called the Labour leader and Sadiq Khan a "negative force" during a press conference with Theresa May.
Appearing alongside the Prime Minister at the Foreign and Commonwealth Office on Tuesday afternoon, Mr Trump took aim the Labour leader, who spoke at a protest against his state visit to the UK.
Answering questions from journalists after their press conference, where Mr Trump and Mrs May paid tribute to the "special relationship" between the two countries, the US President said Mr Corbyn "wanted to meet with me, but I told him no".
Mr Trump added: "I don't know Jeremy Corbyn, I've never met him, never spoke to him, but he wanted to meet today or tomorrow and I decided that I would not do that.
"I think that he is, from where I come from, somewhat of a negative force.
"I think people should look to do things correctly as opposed to criticise... So I decided not to meet."
A Labour spokesperson confirmed Mr Corbyn had reached out to Mr Trump, saying: "Jeremy Corbyn proposed a meeting with Donald Trump during the president's visit.
"Jeremy is ready to engage with the president on a range of issues, including the climate emergency, threats to peace and the refugee crisis."
Despite declining a request to meet with the leader of the opposition, the US president had hinted he would meet the leader of the Brexit Party, Nigel Farage.
Mr Farage, who was pictured being driven to Winfield House, the residence of the US ambassador in London, said he had a "good meeting" with the US President.
The former Ukip leader said the president "really believes in Brexit" and that Mr Trump was "loving his trip to London".
Trump doubles down on 'stone-cold loser' Khan
At the press conference with Mrs May at the Foreign and Commonwealth Office, Mr Trump criticised the Mayor of London again, after calling him a "stone cold loser" earlier this week.
Mr Trump said: "He's not been a very good mayor from what I understand.
"He's done a poor job. Crime is up, a lot of problems. And I don't think he should be criticising a representative of the United States that can do so much good for the UK.
"He should be positive, not negative. He's a negative force. If you look at what he said, he hurts the people of this country."
Mrs May added: "The meeting we've had today are about the future of this most important relationship between the US and the UK.
"As the president described it, it is the greatest alliance this world has ever seen."
During a question and answer session, Donald Trump:
Said Jeremy Corbyn and Sadiq Khan were a "negative force"
Claimed the protests against him were "fake news"
Added the UK "probably should" leave the EU with or without a deal by October 31
The NHS should be "on the table" when it comes to post-Brexit trade talks
Paid tribute to the "special relationship" between the UK and the US
Predicted Huawei 5G would have no impact on UK-US intelligence sharing
'Fake news' to blame for protests
Mr Trump blamed the "fake news" for blowing the scale of the protests out of proportion, insisting he had not seen many protesters taking to the street of London on either day of his two days in the capital.
Mr Trump said: "There were thousands of people on the streets cheering. Even coming over today, there were thousands of people cheering.
"Then as I was coming over today, I heard there were protests but I said where are the protests? I don't see any protests.
"I did see a small protest today when I came, so a lot of it is fake news, I hate to say it.
"But you saw the people waving the American flag, waving your flag, it was tremendous spirit and love. It was an alliance."
UK 'probably should' leave EU with or without a deal by October 31 - as Trump urges May to 'stick around'
Mr Trump - who famously predicted Brexit on the eve of the referendum - said the UK "probably should" leave the EU with or without a deal by October 31.
The US President said he thought Brexit "will happen and it probably should", admitting he thought the vote to leave boiled down to immigration.
Speaking about the UK's future, Mr Trump said: "As the UK makes preparations to leave the European Union, the US is committed to a phenomenal trade deal between the US and the UK.
"There is tremendous potential of that trade deal, I say two or probably even three times what we're doing right now."
He added the UK "probably should" leave the EU by October 31 - with or without a deal.
"I think it will happen and I believe the Prime Minister has brought it to a very good place. I believe it would be good for the country."
Mrs May added: "I continue to believe that actually it is in the interests of the UK to leave the EU with a deal. I think we have a good deal.
"Sadly, the Labour party and other MPs have so far stopped us delivering Brexit and that deal but obviously this is an issue that is going to continue here in the UK."
Mrs May added: "Once we deliver Brexit, and once we are out of the EU, we will be able to do what we've been talking about here today and develop not just that free trade agreement, but that broader economic partnership into the future."
Earlier on Tuesday, Mr Trump urged Mrs May to "stick around" to help the UK secure a "very, very substantial trade deal".
Speaking at a round table talk with business leaders and the Prime Minister at St James' Palace, the US President said a deal can be agreed between the two countries once the UK leaves the European Union.
His comments came just before he arrived at Downing Street, where he and his wife Melania were greeted by Mrs May and her husband Philip outside the steps where Mrs May announced her resignation just a few days ago.
Mrs May said that there were "huge opportunities" for Britain and the US to work together in the future.
"It is a great partnership but I think a partnership we can take even further. Of course that is with a good bilateral trade deal," she said.
Shortly after Mr Trump's comments about striking a trade deal with Theresa May, ITV News Political Editor Robert Peston revealed that the US President had spoken on the phone to Boris Johnson for 20-minutes earlier on Tuesday.
A source close to another leadership hopeful, Michael Gove, added the Environment Secretary may be meeting with Mr Trump today as well, while Brexit Party leader Nigel Farage is also rumoured to be meeting the President.
NHS 'on the table' during post-Brexit trade talks with the US, Trump says
NHS 'on the table' in post-Brexit trade talks, says Trump
Political opponents have rallied against Trump's suggestion that the NHS could be on the table during trade talks with the UK after Brexit.
He said: "I think everything with a trade deal is on the table.
"When you're dealing in trade everything is on the table so NHS or anything else, a lot more than that, but everything will be on the table, absolutely."
Prime Minster Theresa May added: "But the point in making trade deals is of course that both sides negotiate and come to an agreement about what should or should not be in that trade deal for the future."
Labour leader Mr Corbyn, who was attacked by Mr Trump during the press conference, tweeted: "Theresa May stood next to @realDonaldTrump as he said the NHS will be 'on the table' in a US trade deal.
"And that's what Tory leadership contenders and Farage are lining up for the No Deal disaster capitalism plans they have. They all need to understand: our NHS is not for sale."
Conservative leadership hopeful and Health Secretary Matt Hancock said the NHS should be off the table in any talks with Mr Trump.
He said: "Dear Mr President. The NHS isn't on the table in trade talks - and never will be. Not on my watch."
So what's been on the agenda?
Mr Trump is scheduled to head to Downing Street with Mrs May on Tuesday morning for more high level talks, where the pair are expected to discuss a range of issues on which they hold differing views.
However Mrs May's imminent departure has left many questioning the strength of any outcome of the meeting.
It had been thought the two leaders would hold one-to-one meetings, but they will be held with members of each side's teams.
Downing Street has insisted it is not unusual for the two leaders to not have a face-to-face discussion.
Chinese telecoms giant Huawei was on the agenda at the meeting, while pundits also believe climate change, Iran, and the fate of captured so-called Islamic State (IS) fighters were also discussed.
Ahead of the talks, there has been speculation that Mrs May will stand by the reported position of the National Security Council that Huawei products can be used to build "non-core" elements of the 5G network.
However the US has repeatedly warned of the risk to intelligence sharing if any Huawei technology is used over fears it could be exploited by the Chinese state.
Asked if the US could impose limits on intelligence sharing if the UK used Huawei infrastructure, Mr Trump said: "No, because we're gonna have absolutely an agreement on Huawei and everything else.
"We have an incredible intelligence relationship and we will be able to work out any differences.
"We did discuss it - I see absolutely no limitations, we've never had limitations. This is a truly great ally and partner and we'll have no problem with that."
Climate change, something which the US President has referred to as a "hoax" in the past, is also likely to be a topic of discussion.
Mr Trump pulled America out of the landmark Paris Accord which seeks to limit rising global temperatures, while the UK remains committed to it.
Another agreement Mr Trump has pulled the US out of is the Iran Nuclear Deal which aims to limit the Middle Eastern country's ability to create nuclear weapons. Britain, along with four other signatories, remains committed to a 2015 deal signed with Tehran.
What to do with ISIS fighters to fight for could also feature in the talks.
European countries currently have no definite solution on what to do with these people, including those who travelled from abroad to join so-called IS.
Mr Trump has previously called on European countries to take back their detainees.
During his tour of Downing Street, Mr Trump viewed the Sussex Declaration - a rare copy of the American Declaration of Independence on sheepskin parchment dating back to the 1780s.
Trump turns to Tory leadership hopefuls and arch-Brexiteers
Mr Trump's remarks about a possible UK-US trade deal comes as he is reportedly due to meet Conservative leadership hopefuls Michael Gove and Jeremy Hunt.
According to sources close to the Environment Secretary, the meeting is likely to be a one-to-one.
Prior to arriving at the UK, Mr Trump praised another Conservative leadership hopeful, Boris Johnson, which sparked rumours they could also meet during the President's state visit.
ITV News Political Editor Robert Peston said Mr Johnson and Mr Trump had a 20-minute phone call on Tuesday morning, with Mr Johnson turning down the chance to meet the President to take part in a hustings.
At Tuesday's press conference, Mr Trump spoke about all three MPs hoping to take over the reins at Number 10.
Mr Trump said: "I know Boris. I like him. I have liked him for a long time. I think he would do a very good job. I know Jeremy, I think he would do a very good job."
However following earlier rumours of a possible one-to-one meeting with Michael Gove later, Mr Trump admitted he did not know the Environment Secretary.
Turning to Foreign Secretary Mr Hunt, Mr Trump asked: "I don't know Michael - would he do a good job Jeremy?"
Former cabinet ministers and arch-Brexiteers Iain Duncan Smith and Owen Paterson also met with Mr Trump.
The two Tory MPs, who both supported Brexit in the EU referendum, had a meeting which "covered a whole range of subjects including Brexit", a spokesman for Mr Duncan Smith said.
Brexit Party leader Nigel Farage also met with the US President, where Mr Trump said the pair discussed trade.
He said: "My big take from that meeting an hour ago is America is prepared for this and we simply aren't."
Protests around London as May meets Trump
While the Prime Minister hosts Mr Trump, Jeremy Corbyn will be gearing up to address demonstrators “in solidarity with those he’s [the US President] attacked in America, around the world and in our own country”.
The Labour leader, who refused an invitation to Monday evening’s state banquet, is due to be joined by other political parties including members of the Liberal Democrats and the Green Party.
Mayor of London Sadiq Khan defended Corbyn's decision to boycott a state dinner at Buckingham Palace.
The Labour leader attended a state dinner for Chinese president Xi Jinping in 2015 - a country which does not hold democratic elections - but skipped Monday's event.
Asked if Mr Corbyn's views were hypocritical, Mr Khan said: "My views are quite clear and I think Jeremy Corbyn's are not dissimilar which is 'yes we should have a close relationship with the president of the USA, yes he should be able to come here on a working visit'."
While some people protested both for and against Mr Trump outside Buckingham Palace on Monday, Tuesday has seen thousands of activists take to the streets of Whitehall and Trafalgar Square.
In London, the policing operation means the protesters cannot demonstrate outside Downing Street, where the talks between the two leaders will be held.