The Sun said the interview was conducted Thursday in Brussels, before Trump traveled to Britain. Two senior ministers resigned in protest this week at her plans for trade with the European Union after Britain leaves the bloc next March.
The long-awaited document proposes keeping Britain and the European Union in a free market for goods, with a more distant relationship for services.
After spending the night at the United States ambassador's official residence in Regent's Park, London, the USA president will join the Theresa May at a military base on Friday to view a joint counter-terrorism exercise involving UK and U.S. special forces.
Criticising May for the warm welcome given to the American leader, he said: "Theresa May has invited President Trump to our country at a time when his unsafe and inhumane policies are putting the lives and wellbeing of millions of people at risk".
Jacob Rees-Mogg - a leading Conservative Brexiteer and considered a potential alternative party leader by some - said it was perfectly reasonable for Trump to make such comments, adding that May now had an opportunity to change her mind on her Brexit plan.
"I would have done it much differently".
As for Johnson, Trump said: "I think he would be a great prime minister".
Johnson isn't the only politician to have quit over May's Brexit plans, as ministers David Davis and Steve Baker also quit the government in protest.
The Trumps landed at Stansted Airport, Essex, at 13:50 BST before a helicopter took them to Winfield House in Regent's Park, where they are staying as guests of the USA ambassador.
Trump predicts some North Atlantic Treaty Organisation allies buy from United States defense contractors
Macron said France, which a year ago spent 1.8 percent on defence, would meet the target by the 2024 deadline. Nonetheless, he has simultaneously asserted that the USA should pay less.
Only 4 Days in, China-US Trade War Escalates
Trump on Wednesday framed his trade actions as necessary to shield American businesses and farmers from harmful trading practices. So what can China do? Donald Trump's threat to impose tariffs on an extra $200bn of Chinese imports is causing rising anxiety.
Vietnam Airlines adjusts Taiwan flights due to Typhoon Maria
Typhoons normally hit Taiwan, China, Japan , the Philippines and Vietnam from June through November each year. Across the Taiwan Strait, schools and factories in coastal areas of the Chinese province of Fujian are closed.
Trump, in an interview with The Sun newspaper, said he felt unwelcome in London because of protests, including plans to fly a giant balloon over Parliament on Friday that depicts him as an angry baby in a diaper. I know they have had a lot of resignations.
"I would say Brexit is Brexit", he added. "I think you are losing your culture".
He lashed out again at North Atlantic Treaty Organisation and resumed his feud with London Mayor Sadiq Khan.
"I used to love London as a city", Trump said.
On Saturday, Trump supporters will rally near the U.S. embassy in Nine Elms, south London, for an event titled "Welcoming Trump to Britain Rally - Make Britain Great Again", at which a number of right-wing figures are scheduled to speak.
"I cherish the special relationship with the USA and the many Americans who contribute to our city", posted Khan, London's first Muslim mayor.
Protests took place outside the Blenheim grounds in Woodstock, Oxfordshire, with several hundred demonstrators waving banners and placards reading Dump Trump, Not Welcome Here, Protect Children Not Trump and Keep Your Tiny Hands Off My Pussy! Melania Trump, 48, isn't amused by the way the Londoners are going to greet her husband.
"I think he has done a bad job on crime, if you look, all of the terrible things going on there, with all of the crime that is being brought in", he said.
"I was very saddened to see he was leaving government and I hope he goes back in at some point".
Asked if he could become prime minister he added: "Well I am not pitting one against the other". "I think it changed the fabric of Europe and, unless you act very quickly, it's never going to be what it was, and I don't mean that in a positive way".