The Black Lives Matter protest was called off amid fears of clashes with right-wing counter-protesters, who have been clashing violently with police for the last few hours.
In central London, demonstrators have clashed with police close to Westminster Bridge, with glass bottles thrown towards the officers and their vans, PA Media reports.
other demonstrators gathered around the Cenotaph war memorial in Whitehall and the boarded-up statue of Winston Churchill in Parliament Square on Saturday.
Various groups from around the country, including right-wing activists and groups formed of football supporters, said they had come to London to protect symbols of British history.
Among the demonstrators was Paul Golding, leader of the far-right group Britain First, who said they had turned out to "guard our monuments".
The statue of Churchill was boxed up to protect it from potential damage, after protesters daubed "was a racist" on it last weekend.
Protesters sang the national anthem and chanted "England", amid a tense atmosphere and heavy police presence.
One large group moved to barricades outside Downing Street and a number of objects were thrown towards police.
Sharing footage of the clashes on Twitter, Home Secretary Priti Patel described it as "unacceptable thuggery".
"Any perpetrators of violence or vandalism should expect to face the full force of the law," she wrote.
"Violence towards our police officers will not be tolerated."
She added that coronavirus "remains a threat to us all", urging people to go home.
The Met Police said it had put a Section 60 order in place until 02:00 BST on Sunday, giving officers enhanced powers to stop and search individuals.
The Met said the move came after it learned some people were coming into London to cause harm and were likely to bring weapons with them.
Earlier, police urged protesters not to attend demonstrations in the capital due to the pandemic.
"We are asking you not to come to London, and let your voices be heard in other ways," Met Commander Bas Javid said.