'Exercise caution if unexpectedly in the vicinity of large gatherings that may become violent, ' it said.
Meanwhile, London Mayor Sadiq Khan has granted permission for a giant inflatable figure depicting Mr Trump as a baby to fly over Westminster for two hours on the second day of the president's visit.
"We don't know when".
The request as Trump is expected to meet with multiple protests during his first visit to the country since taking office.
The protest will continue on July 14 when a "carnival of resistance" is scheduled to take place in Edinburgh, coinciding with Donald Trump's visit to the UK.
In the busy south London neighborhood of Brixton, Victor Greetham, who runs a jazz bar, said he hasn't been to a demonstration since he protested against the Iraq War in 2003, but he planned to attend one of the protests against Trump's visit.
While Trump is expected to have a busy schedule throughout his visit, there is at least one place that he will avoid: central London.
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Ms Elliott, who has lived in London for five years, appealed to anyone out demonstrating to "respectfully disagree" after a warning from the United States embassy in London of potential violence.
Trump "has proudly sparked passionate often divisive emotions about things, I think Americans living here to eager to turn out and express their views", he said.
The U.S. president is also due to travel to Scotland where he owns two golf courses and Scotland's interim police chief has said more than 5,000 officers would be needed for to cover the trip, including specialist riot and armed officers.
Mrs May will be seeking to improve her often publicly strained relationship with the United States president as she pushes for a post-Brexit trade deal with the US.
Temporary signs indicate road closures around the USA ambassador's residence, where special fences have been erected prior to the US presidential visit at the end of the week, in Regent's Park in London, Britain, July 10, 2018.
Following his meeting in Brussels for the North Atlantic Treaty Organisation summit today, Mr Trump will fly into London tomorrow, Thursday, July 12.
While Mr Johnson may now be a backbencher, Mr Trump said he hoped he would still see the former foreign minister - another blow to the fragile position of Mrs May.
Tension could also be sparked as Mrs May expects the USA president to remember the "malign behaviour" of Russian Federation when he meets Mr Putin.