Senior cabinet ministers David Davis and Boris Johnson quit this week over her plans for trade ties with the European Union after Britain leaves the bloc next March.
It has been dubbed Storm Trump and the country is braced for a United States presidential visit that has split opinion like never before.
Awaiting him on the tarmac were three MV-22 Osprey helicopters belonging to the US Marines which are used to transport his staff and security detail on overseas trips.
Asked about Trump's comments, May said: "We're delivering on the vote of the British people to take back control of our money, our laws and our borders".
USA ambassador Woody Johnson insisted the balloon was not a fair representation of British views. "Everywhere he goes there are protests, so I don't think it really makes a big impression on him".
More than 60,000 people have signed up to demonstrate in London on Friday when protesters intend to fly a large balloon over parliament portraying Trump as an orange, snarling baby.
The crowdfunded initiative has been dubbed "Trump Baby".
George Clooney involved in scooter accident in Italy
This caused him to be knocked off the scooter, and the driver of the auto that cut him off stopped and called for an ambulance. He is understood to have received treatment at John Paul II hospital, but NBC News report that he has since been discharged.
The US president's brash style and hard line "America First" policies have caused consternation across Britain's political spectrum and society.
His criticism of Britain's anti-terror policies after a series of attacks in 2017 also did not go down well.
Opposition MPS, backed by an online petition signed by almost 1.9 million people, called on May to cancel the state visit offered when she met Trump in Washington after his inauguration in January a year ago.
It has vowed to gather near the USA ambassador's residence in London, where Trump and First Lady Melania Trump will stay Thursday night, and outside Blenheim Palace, wartime leader Winston Churchill's birthplace, which hosts the pair for dinner prior.
On Friday, demonstrators are expected to gather near Chequers, the Prime Minister's country residence, where May and Trump will hold a working lunch.
Russia, Brexit and the Middle East are set to top the agenda.
President Trump will head to London on Friday, where he's expected to face protests at every turn.
"It's typical, but honestly Donald Trump's legacy will outlive any big orange balloon and the matters that will be discussed at Chequers and now in Brussels are much more important and will have a much longer effect than any day rally", she said. May will host Trump and tuxedo-clad government ministers and representatives of fund managers BlackRock and Blackstone Group, as well as Arup and drinks manufacturer Diageo, for a dinner of Scottish salmon, beef and strawberries and clotted cream ice cream to discuss post-Brexit trade.