In an extraordinary interview with a British newspaper, Mr Trump said that the PM's plans for a soft Brexit would end any hopes of a trade deal with the USA and suggested that former foreign secretary Boris Johnson, who quit her cabinet earlier this week, would be a better leader than Mrs May.
The comments, following on from the morning press conference, will be a cause of great concern for Mrs May.
In an interview with The Sun newspaper, published on Friday morning, Mr Trump said Ms May's plans for a business-friendly Brexit would leave it too close to the European Union to allow a new trans-Atlantic trade deal to be struck.
Addressing the 100-strong group the Prime Minister said there was an "unprecedented" opportunity to do a deal that boosted jobs and growth in both countries.
May's plan "will definitely affect trade with the United States, unfortunately in a negative way".
Ms May's "business-friendly" Brexit plan - which would keep Britain in a free trade zone for goods with the European Union but mean it has to share some European Union rules - was agreed by her cabinet only last Friday after two years of wrangling since Britons voted to leave the bloc in a 2016 referendum.
A trade deal with the United States is one of the main aims of Brexit supporters within May's Conservative Party, who are concerned that she is making too many concessions to the EU.
Sending a direct warning to the EU, Mr Gill said: "If the EU then demanded we couldn't begin negotiations with other countries we should refuse to apply the EU's tariffs for them on products ultimately destined for the continent".
Mr Trump's intervention comes at the end of a tumultuous few days for Ms May.
But it also says that because of the deep cross-Channel links, "equivalence" is not good enough either.
"The people voted to break it up (Britain's ties with the EU)", Trump said.
But even before Trump arrived in the United Kingdom he attacked May's Brexit plan, saying the country was in "somewhat turmoil" and that meeting Russian President Vladimir Putin next week - her geopolitical enemy - would be easier than meeting her.
Johnson resigned as foreign secretary on Monday, in protest over May's proposal for a "soft" Brexit from the European Union. "I think he has done a bad job on crime, if you look, all of the disgusting things going on there, with all of the crime that is being brought in".
"I would have done it much differently". "I am just saying I think he would be a great prime minister. I think he's got what it takes", he added.
The Trumps had earlier arrived at Stansted with their sizeable entourage. Anyone who takes a close look, however, will see that this largely corresponds to an approach that the Swiss government is now trying out.
The President and First Lady are also slated to meet with the Queen on Friday in Windsor.
Some carried placards saying Special Relationship?
But they avoided the noise and spectacle of the protests on the ground by travelling by helicopter between the airport, London and Oxfordshire.
They were given a best-of-British dinner, featuring Scottish salmon, Hereford beef fillet and strawberries with clotted cream ice-cream.
They were booed and jeered as their helicopter left Regent's Park, with protesters who had gathered to demonstrate against the president's visit shouting "shame on you" and banging pots and pans, in the hope he would hear them from behind the fence erected around the perimeter of Winfield House.
Trump is due to stay overnight at Winfield House, where demonstrators plan to play recordings of migrant children held in U.S. detention centres.