Asked how he felt about the protests, Trump said he was "fine with it".
"I'd like to see them be able to work it out so it could go quickly", he said.
Donald Trump and wife Melania have been pictured dressed up to the nines at a lavish dinner at Blenheim Palace, hosted by Theresa May.
Trump will spend the weekend at the former, which he described as a "magical place", before heading to Helsinki, Finland, for a much-anticipated summit on July 16 with Russian President Vladimir Putin.
"The people voted to break it up (Britain's ties with the EU)", Trump told a press conference.
As US President Donald Trump landed in Britain on Thursday afternoon, protesters were in battle-preparation mode, with demonstrations planned for every stage of his visit.
Trump will depart the North Atlantic Treaty Organisation summit in Brussels on Thursday afternoon local time and head to London for a greeting ceremony.
A YouGov poll on Wednesday showed 77 percent of Britons had an unfavourable opinion of the president and just 50 percent thought his visit should go ahead.
London Mayor Sadiq Khan, a frequent Trump critic, gave his approval for the balloon to be floated, with a spokesperson saying last week that the mayor "supports the right to peaceful protest and understand that this can take many different forms".
"They like me a lot in the United Kingdom", he added.
On Friday, Mrs May and Mr Trump will go to watch a joint counter-terrorism exercise by British and USA special forces at a military base.
The declaration was unusual given the topic being discussed was whether the President would support a Hard Brexit for the UK.
May hopes Trump, who landed at Stansted airport before flying by helicopter to the USA ambassador's London residence, will help to accelerate a future free trade deal, though his public comments on Brexit cast a shadow over the visit.
"I would be happy to see Hillary Clinton if she was president visit the UK".
"I think that [the British] people like me a lot and agree with me on immigration".
On Friday, demonstrators are expected to gather near Chequers, the Prime Minister's country residence, where May and Trump will hold a working lunch.
The bulk of the activity will take place in London, where people plan to gather first in Regent's Park outside of the US ambassador's house on Thursday and again across central London for a series of protests throughout the day on Friday.
We're more than used to our best sports-stars and celebrities being picked up as "British" in the English media when they're on the rise, and "Irish" when they're underperforming or in trouble.