That led roughly 500,000 people to sign a petition calling for Trump to be banned from entering the Britain.
The extra security measures may strike Londoners as incongruous, set amid the leafy surrounds of Regent's Park, a spot popular with joggers, picnickers and families.
Speaking to reporters at an emergency press conference after intense North Atlantic Treaty Organisation talks, the comment was made as he was asked about Brexit and the prospect of protests on his United Kingdom visit.
On reaching the residence the pair walked across the lawn hand-in-hand. Many will see his avoidance of London as proof he is trying to keep away from dissent, however, the United States ambassador to the UK, Woody Johnson, denied this.
"The President is not avoiding anything", he said.
The US Embassy in Britain has urged Americans to "keep a low profile" during the president's visit to London.
Many Britons are opposed to Trump's trip which is not the full state visit he was originally promised with the pomp and ceremony that entails.
Demonstrators have lined the streets outside Blenheim Palace in Oxfordshire where Mr Trump and his wife Melania are attending a black tie dinner.
They stood with the Mays to listen to the bandsmen of the Scots, Irish and Welsh Guards, who played the Liberty Fanfare, Amazing Grace and the National Emblem.
Trump may not be able to ignore the presence of protesters entirely.
May has had to defend Trump's visit in the face of fiery criticism from opposition lawmakers. "Be aware of your surroundings (and) exercise caution if unexpectedly in the vicinity of large gatherings that may become violent", it added.
The president has at his side at all times a White House doctor and one of five rotating military aides who carry the nuclear "football" - equipped with communication tools and a book with prepared war plans. Mr. Trump has been a keen supporter of Brexit and on Thursday he appeared to echo those concerns.
"We urge that the Scottish Government rules out any use of Prestwick by the president or his entourage, and so send the most powerful message possible that Donald Trump is not welcome in Scotland". She also plans to shift the focus during the rest of Mr. Trump's visit, hoping to steer him toward talk about trade and the growing threat of Russian Federation. They like me a lot in the UK.
"I've been reading a lot about Brexit over the last couple of days".
But, he added: "Whether he sees it, whether he reacts to it, we don't really care. I was happy when Obama did it".
A giant six-metre-high blimp of Trump depicted as an orange baby in nappies is also expected to fly over the capital.
A YouGov poll on Wednesday showed 77 percent had an unfavorable opinion of the president and just 50 percent thought his visit should go ahead. The UK's speaker of parliament made clear that Trump, because of his values, would not be invited to address MPs.
Perhaps in a reference to Mr Trump's meeting with Vladimir Putin on Monday, she said that Britain and the U.S. work closely together in the interests of their shared security, "whether through targeting Daesh [Islamic State group] terrorists or standing up to Russian aggression".