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Anti-racism protests have been "subverted by thuggery" that betrays their cause, the prime minister has said.
Boris Johnson was speaking after trouble flared for a second day in central London, with police drawing their batons and scuffling with protesters as they tried to force their way through to a restricted area.
Police were forced to run as bottles were thrown near the stone arches at the junction of King Charles Street and Whitehall.
Eight officers were injured after the trouble started at around 7.30pm on Sunday with the Met Police saying 12 people were arrested for public order offences.
The prime minister tweeted: "People have a right to protest peacefully & while observing social distancing but they have no right to attack the police.
"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."
A statue of a slave trader and merchant, which has been the subject of an 11,000-strong petition to have it removed, was also pulled down and dumped in the harbour in Bristol.
It came a day after 14 police were hurt in clashes on London's Whitehall - near The Cenotaph and Downing Street, with officers on horseback forced to charge at troublemakers.
Sky correspondent Mark White said Sunday's disorder continued into the night as several small groups set bins alight, smashed windows and threw bottles as police tried to enforce a dispersal notice in Westminster.
The earlier flare-up, involving about a few hundred protesters, came amid a second day of mainly peaceful demonstrations in UK cities.
People took to the streets of cities such as Edinburgh and Manchester to support the Black Lives Matter movement and call for justice over the killing of George Floyd in America two weeks ago.
Elsewhere, the operational patrol unit of Warwickshire Police tweeted that the M6 southbound was temporarily closed shortly after 6pm due to pedestrian protesters blocking the carriageway at Junction 3.
The force said the M6 began to reopen an hour later, as demonstrators "headed into Coventry at Junction 2".
Thousands of people with cardboard placards descended on the US embassy in London, with the crowd snaking down the road and chanting for justice and equality.
Free masks, gloves and hand gel were being given out amid concerns from the likes of the health secretary - who told Sky News the protests could lead to a rise in coronavirus infections.
In Bristol, a controversial statue of Edward Colston - who made his fortune off the back of the slave trade - was pulled down to huge cheers and dumped in the harbour.
Home Secretary Priti Patel called it "utterly disgraceful" and an act that distracted from the protesters' cause.
Police said it was toppled by a "small group of people" who they were working to identify and that there were "no instances of disorder" or arrests among the estimated 10,000 protesters.
A statue of Sir Winston Churchill was also defaced in Westminster, with the words (Churchill) "was a racist" daubed on the plinth.
Demonstrations have been going on around the world after George Floyd, 46, was killed in Minneapolis on 25 May when a white police officer knelt on his neck for nearly nine minutes - despite his repeated pleas that he could not breathe.