He said it was different to when former United States president Barack Obama tried to help the Remain campaign during the 2016 European Union referendum campaign by saying the UK would be at the "back of the queue" for a trade deal with the USA if left the EU.
Downing Street has not yet reacted to Mr Trump's remarks.
U.S. Ambassador Woody Johnson said Wednesday that citizens are often advised to avoid public demonstrations and that he is not upset by the decision to allow the "Trump baby" balloon to be displayed near Parliament.
US President Donald Trump said a free trade deal with Britain might be impossible if it went ahead with Prime Minister Theresa May's proposals for post-Brexit ties with the European Union, in a damaging intervention set to further criticism of her plans. He said they spent about 90 minutes talking at dinner and claimed they "probably never developed a better relationship than last night".
The comments, following on from the morning press conference, will be a cause of great concern for Mrs May.
The president downplayed the fallout from the interview as he next to May on Friday for a bilateral meeting at Chequers, her official country house.
Britain would leave the EU's single market and customs union as planned, to end free movement of people and sign its own non-EU trade deals.
He told The Sun Mrs May's plan would affect trade "unfortunately in a negative way".
"We have enough difficulty with the European Union. People see him as a cheap huckster who happens to have an office we respect as president of the United States".
Speaking to BBC Radio 4's Today programme, Mr Ruddy said: 'Trump will think the baby balloon is about him so it's probably a positive thing.
"I would have done it much differently", Trump told The Sun newspaper in an explosive interview just hours before rubbing elbows with the British leader at a lavish black-tie dinner at Blenheim Castle in Oxfordshire.
Asked about his trip to the UK, Trump said he was not concerned about protests because "they like me a lot there", suggesting the Brexit vote had come about because "they agree with me on immigration".
"I told them I would be very unhappy if they did not up their commitments substantially".
He added that it seemed as if the United Kingdom was "getting at least partially involved back with the European Union". "They are just a lobbyist for Amazon", he said.
The timing of the comments could not be worse for May, who is fighting a rebellion among her own MPs over Brexit which has seen Brexit secretary David Davis and foreign secretary Boris Johnson quit her government.
"I'm not pitting one against the other", Trump said. "I think he's got what it takes".
"With the flexibility that is built into the white paper proposals, there is absolutely no reason why a trade deal between us and the USA can not happen and I think both sides do want it to happen". Their first interaction after the publication of the interview.
He landed at Stansted Airport Thursday afternoon and was whisked by helicopter to Winfield House, the American diplomatic residence in London.
"Donald Trump is a big, angry baby with a fragile ego and tiny hands", the group's fundraising page reads.
Trump and his wife Melania are due to meet the 92-year-old monarch at Windsor Castle on Friday and both the imposing setting and Elizabeth being one of the most admired women in the world is expected to temper the U.S. president's iconaclastic ways.