Theresa May and Donald Trump’s relationship is “very, very strong”, the US president has said, following his controversial comments on Brexit.
Speaking at the PM’s Chequers retreat, Mr Trump said his first official UK visit was “really something”.
Meanwhile, a blimp of Mr Trump as a baby is floating above central London.
It is part of a demonstration against the US president in Parliament Square, one of many due to take place across the UK on Friday.
Speaking before bilateral talks on Friday, Mrs May said she and Mr Trump had “a lot to discuss” including the “special relationship” between the UK and US and a possible trade deal.
“And of course we will discuss foreign policy and defence and security issues, where we work really closely together with the US,” she said.
Mr Trump said they had “just looked at some incredible anti-terrorism things that are being done here in conjunction with the United States”.
He said he and Mrs May “spoke for an hour or an hour and a half” at the black-tie dinner which he attended with wife Melania at Blenheim Palace on Thursday evening..
“I think we probably never developed a better relationship than last night,” he said.
It was during the dinner on Thursday evening that the Sun published an interview with Mr Trump that had been conducted in Brussels earlier this week.
In the controversial interview, Mr Trump said that former Foreign Secretary Boris Johnson – who disagrees with the PM on Brexit and resigned this week – would make a “great prime minister”, adding “I think he’s got what it takes”.
He also renewed his criticism of London Mayor Sadiq Khan over last year’s terror attacks in London, saying he had done “a terrible job”.
Downing Street has not yet reacted to Mr Trump’s remarks, but Chancellor Philip Hammond said the Chequers talks would be “very positive”.
After it was published, White House spokeswoman Sarah Sanders said the president “likes and respects Prime Minister May very much”, adding that he had “never said anything bad about her”.
Mr Trump – who has been a long-time supporter of Brexit – also said Mrs May had not listened to his advice on how to do a Brexit deal, saying: “I would have done it much differently.”
Tom Newton Dunn, the Sun journalist who interviewed Mr Trump, said the US president seemed “sensitive” and knew about the “Trump baby” inflatable.
“He’s really quite stung by the criticism he’s been getting,” said Mr Newton Dunn. “He knew all about the baby blimp. I think it hurt him.”
Mr Trump arrived at Chequers by helicopter after visiting the Royal Military Academy Sandhurst on Friday morning.
He and Mrs May will hold a joint press conference following their talks.
Meanwhile, First Lady Melania Trump played bowls with the PM’s husband, Philip May, at the Royal Hospital Chelsea in London. She met Chelsea pensioners and local children.
Extra security is in place to police protests planned for the second day of Mr Trump’s visit.
The president and first lady will travel to Windsor on Friday afternoon to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump’s Turnberry golf resort. This part of the visit is being considered private.
Responding to Mr Trump’s interview, Foreign Office minister Sir Alan Duncan said the government does not see Mr Trump’s behaviour as “rude”, said Sir Alan, adding: “Donald Trump is a controversialist. That’s his style.”
Mayor of London Sadiq Khan defended his decision to allow the giant Trump baby inflatable to fly over London, saying: “The idea that we limit the right to protest because it might cause offence to a foreign leader is a slippery slope”.
And, responding to Mr Trump’s criticism of his response to terrorism, Mr Khan said it was “interesting” that he “is not criticising the mayors of other cities” which have also experienced terror attacks.
Meanwhile, Shadow Foreign Secretary Emily Thornberry said the PM “should be standing up to [Mr Trump]” after he “slagged her off”, instead of holding his hand.