Arriving straight from a North Atlantic Treaty Organisation summit that was predictably contentious, the U.S. president has been greeted with massive protests on his first trip to London since taking office.
Such comments are likely to be seen as unwelcome by Mrs May, who has already faced significant political criticism for hosting Mr Trump.
May, in contrast, praised immigration for the benefits it had brought to the UK. "Just make sure you can trade with us, that's all that matters", he said to May.More news: Kellogg's Honey Smacks: officials warn against cereal after salmonella outbreak
Farage, a member of European Parliament and former leader of the U.K. Independence Party, said Trump made a decision to "intervene" for two reasons: he believes in Brexit and he feels the USA has been let down.
"But at times where we think the other side is not meeting the high standards we expect of each other we shouldn't be afraid of calling them out - that's like having a best mate".
In his Sun interview, Mr Trump also said 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".
"We agreed today that as the United Kingdom leaves the European Union we will pursue an ambitious U.S. -UK free trade agreement", she said.
Trump described Johnson as a "talented" and "very supportive friend" who would "make a great Prime Minister". And since bullies only respond to strength, from now onward I should be prepared to be much stronger. "She wanted to go a different route", he told the paper. He was decidedly critical of May and her Brexit plan, saying he "would have done it much differently".More news: Croatia not just about Modric | FIFA World Cup | Croatia | France | Modric
On Friday he rephrased his account, saying that he had given "a suggestion" to May over Brexit, not advice.
In the wake of the interview, White House press secretary Sarah Sanders issued a statement that appeared aimed to smooth things over. "I think he has done a very bad job on terrorism", Trump said, according to The Guardian.
He added that he supported the resignations of Mr Davis and Mr Johnson, and said the Tories were telling businesses that "the rules that have burdened you for year are not going to go anywhere".
"We are cracking down right now on the European Union because they have not treated the United States fairly on trading".More news: Trump scolds Europe on gas