There are fears that demonstrations over Trump's three-day visit to the United Kingdom, where he will meet with British Prime Minister Theresa May and Queen Elizabeth, could turn violent.
The notice asks for Americans in Britain to stay aware of their surroundings and to "exercise caution if unexpectedly in the vicinity of large gatherings that may become violent".
The National Police Chiefs' Council said discussions were ongoing about "how the resource requirements of this massive operation will be met" but a spokesman said: "We are confident that forces will continue to maintain local policing services".
The request as Trump is expected to meet with multiple protests during his first visit to the country since taking office.
President Trump lands in London on Thursday night for a dinner in his honour at Blenheim Palace in Oxfordshire.
As anti-Trump activists demonstrate during the United States president's visit, supporters will gather in the British capital to welcome him to Britain.
"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.
On the NHS: Trump said it was "going broke and not working".
The state visit has never actually been scheduled - there is fierce opposition to it in many quarters of Britain - and this trip is part of a working visit instead, meaning among things that Trump will overnight at Winfield House, the USA ambassador's handsome residence near Regents Park rather than in Buckingham Palace or Windsor Castle as a guest of the queen.
Mr Trump tweeted of his visit cancellation: "Reason I canceled my trip to London is that I am not a big fan of the Obama Administration having sold perhaps the best located and finest embassy in London for "peanuts", only to build a new one in an off location for 1.2 billion dollars".
She said: "I think he means to put America first and I think he's been doing that and he's been very consistent with his campaign promises".
Then on Monday, he will be off to Helsinki to meet with Russian President Vladimir Putin.
He also said he might speak to Boris Johnson, who quit as foreign secretary over May's plans for a business-friendly Brexit which was only agreed by her cabinet last Friday after two years of wrangling.
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