Donald Trump's July visit to the UK will be his first as president of the United States.
Some cited "job restrictions" while another said he was wary of the press.
"She should negotiate the best way she knows how", Trump continued.
The US president's brash style and hard line "America First" policies have caused consternation across Britain's political spectrum and society.
British pageantry was on grand display Thursday as President Donald Trump and first lady Melania Trump arrived on the historic grounds of Blenheim Palace for an exclusive black tie gala hosted by Prime Minister Theresa May.
Speaking at a press conference following a North Atlantic Treaty Organisation summit in Brussels, the president said he thought the vote for Brexit was primarily due to concerns about immigration.
When asked about Trump's remarks, May said in Brussels: "What we are doing is delivering on the vote of the British people... that's what our proposal does". "I just want the people to be happy".
In a statement ahead of Trump's arrival, she said the visit would focus on trade and strengthening defence and security ties, saying there was no stronger alliance than Britain's "special relationship with the U.S.".
After London, he will travel to Scotland and then onto Helsinki to meet with Russian president Vladimir Putin. The UK's speaker of parliament made clear that Trump, because of his values, would not be invited to address MPs. Vince Cable, the leader of the pro-EU Liberal Democrats, said, "Most of us don't think he is particularly good judge on Brexit or anything else".
At the time the Prime Minister's spokesman said: "If you watch the video, they're walking along and there is an unseen ramp".
John Scardino, 58, a high school teacher from the United States who has lived in Britian for 18 years and will be at Friday's protests in London, is dubious that the embassy alert would have any effect on crowd size.
Protesters were expected to rally during his visit.
Protests are planned across the city and extra security has been put in place to police the demonstrations.
Dick said: "We will keep him safe".
Lead guitarist Geoff Sprinks said: "We will not be anywhere near where he's going to be, it would be lovely to have played at one of the protests".
President Trump will head to London on Friday, where he's expected to face protests at every turn.
Command suites and coordinating groups based in Lambeth, south London, will involve a wide range of people including from all the emergency services, the military, Foreign Office and Home Office, plus officials who run transport services in London and beyond.
The British are usually polite to a fault - though they have been known to go off after a soccer match or once the pubs close.
He added that "it seems to be turning a little differently where they seem to be getting partially backed involved with European Union". They will be doing that in concert with the Civil Aviation Authority, the US Air Force and the RAF.
"They trust us on issues to do with nuclear missiles in a way that they don't trust any other country".
Dick also said the workforce which is having to "flex, surge and to respond" to events is made up of "fantastic people with a clear sense of mission, high skills and wonderful ethics".
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".