The US president and First Lady Melania Trump were given a red carpet reception at Blenheim Palace in Oxfordshire, where the prime minister pressed her case for an ambitious new trade deal after Brexit.
Addressing Mr Trump in front of an audience of business leaders at Winston Churchill’s birthplace, Mrs May insisted that Brexit provides an opportunity for an “unprecedented” agreement to boost jobs and growth.
And in an apparent plea to the president to remember his allies when he meets Vladimir Putin on Monday, Mrs May noted that Britain and America work closely on security “whether through targeting Daesh terrorists or standing up to Russian aggression”.
In a scene reminiscent of their White House meeting last year, the UK and US leaders held hands as they walked up steps to the palace to watch the bands of the Scots, Irish and Welsh Guards.
The Trumps arrived at the grounds on the president’s Marine One helicopter and therefore avoided the estimated 1,000 protesters gathered outside.
Scores of noisy demonstrators also turned up outside the US ambassador’s residence in Regent’s Park in London, where the president and first lady are spending the night.
Mr Trump and his wife landed at Stansted Airport on Thursday afternoon for the start of a four-day trip to the UK, his first since taking office in 2016.
The couple then flew by helicopter to the US ambassador’s residence, Winfield House, where The Beatles’ song We Can Work It Out was playing in the garden on their arrival.
On Friday, Mr Trump will again meet Mrs May at the Royal Military Academy in Sandhurst to watch a military demonstration.
The president and first lady will then head to Windsor Castle to meet the Queen before leaving for Scotland in the evening.
Thousands of people are expected to join two large demonstrations in London, while a “blimp” of Mr Trump as a snarling baby is due to be flown near parliament on Friday morning.
Mayor of London Sadiq Khan has urged those attending the protests not to cause trouble.
“My message to those coming to the protests in London is that this must be peaceful and good-spirited,” he said.
“To those intent on causing trouble or breaking the law, I simply say: you are not welcome.”
A police chief apologised after it was revealed officers securing Mr Trump’s visit to the UK were being forced to sleep in conditions described as an “absolute disgrace”.
Hundreds of officers were to stay in cramped lines of camp beds filling a vast gymnasium and sleeping mats on the floor of squash courts between long shifts policing the US president’s trip.
Essex Police’s assistant chief constable Pippa Mills accepted the conditions were “not acceptable” and said alternative accommodation had been found.