"If they do that, then their trade deal with the US will probably not be made", Trump said.
The UK hopes to make progress on a post-Brexit trade relationship, although the scope for a bilateral trade deal would be limited if the UK remains aligned with European Union regulations on goods.
Trump's interview with British tabloid The Sun was published on the same day he arrived in London, shortly after May revealed plans for a still semi-cozy working relationship between the United Kingdom and the European Union even after Brexit is finalized.
Before the Sun interview was published, May invoked Winston Churchill as she addressed Trump and business leaders at a black-tie dinner at Blenheim Palace, the grand 18th-century country house which was the British World War Two leader's birthplace.More news: Crowning glory for Netflix with Emmy nomination success
While he added that he thought Johnson would one day be a good candidate to lead the country, he insisted that he wasn't trying to put Johnson against May.
Mayor of London Sadiq Khan during London Tech Week in London, on Monday. "I think you are losing your culture".
Sterling fell half a percent to a 1-1/2 week low of $1.3131, partly on Trump's comments. "I think he has done a very bad job on terrorism".
In this photo taken on Tuesday, July 10, 2018, a six-meter high cartoon baby blimp of U.S. President Donald Trump stands inflated during a practice session in Bingfield Park, north London.
Shortly after he told North Atlantic Treaty Organisation he didn't think the Brexit deal Mrs May was offering was the one people wanted, he continued to lay into the British prime minister, even backing her former foreign secretary Boris Johnson to be a successor. Hundreds of protesters descended on the castle to voice their opposition to the president's visit. Although Trump has said this practice will be stopped, thousands of children remain separated from their parents and face great difficulty locating their relatives.More news: Typhoon Maria landed in coastal regions of Huangqi Peninsula, Fujian
"From the public, the welcome will be far from warm", he told lawmakers on Wednesday, noting there would be protests across the country against Trump's "abysmal record on human rights, his repugnant attitude toward women and his disgusting treatment of minorities".
"I would actually say that she probably went the opposite way".
While he stressed he did not want to get involved in the UK's internal affairs, he added: "The people voted to break it up so I would imagine that's what they would do, but maybe they're taking a different route". He then reminded the press that his mother was from Scotland. 'You go through certain areas that didn't exist ten or 15 years ago.' He added: 'Allowing the immigration to take place in Europe is a shame'. "I am not banning the pro-Trump demo either".
British law requires any petition supported by more than 100,000 people to be considered for parliamentary debate, even though there was no serious attempt to prohibit Trump from entering Britain.
The tight security surrounding the visit will attempt to avoid exposing Trump to planned protests in central London.More news: Sharif loyalists arrested as former PM returns to appeal conviction
The prime minister is also likely to face some opposition in Brussels, where officials have repeatedly warned Britain to lower its expectations about how close ties can be.