Boris Johnson said the anti-racism demonstrations had been “subverted by thuggery” following a day of protests across the UK.
Crowds of demonstrators wore face coverings and held placards outside the embassy in Battersea, south-west London, on Sunday, in protest against police brutality following the death of George Floyd in Minneapolis.
While Saturday saw clashes between police and protesters at Whitehall, during which 14 officers injured. Twenty-nine people were arrested.
“People have a right to protest peacefully & while observing social distancing but they have no right to attack the police,” the Prime Minister tweeted.
“These demonstrations have been subverted by thuggery – and they are a betrayal of the cause they purport to serve.
“Those responsible will be held to account.”
Police tactics have come under criticism after mounted officers charged protesters on Saturday.
During the resulting melee one officer was seriously injured after her horse ran her into a traffic light.
Labour MP Zarah Sultana said: “The videos circulating of police on horseback charging on protestors in London are disturbing.
“It is also unacceptable protestors and legal observers were kettled until 1:30AM.
“This will be seen as an attempt to intimidate and deter legitimate protest.”
Similar scenes were not repeated on Sunday, although there were some light skirmishes between police and a minority of protesters.
However, a statue of a 17th Century slave trader was pulled down and dumped in the sea following a march in Bristol.
The bronze memorial to Edward Colston, situated in the city centre since 1895, was torn down after crowds left the city’s College Green and later was dumped into Bristol harbour.
It came after 10,000 people took part in the Black Lives Matter demonstration, which was praised by Avon and Somerset police for being “peaceful and respectful”.
No arrest were made, but officers are now said to be collating footage of a “small group of people” who were filmed pulling down the statue with ropes, which police say amounted to criminal damage.
Meanwhile, the Winston Churchill statue in London was defaced with “was a racist” by a protester.