Home Secretary Priti Patel has said “justice will follow” some of the violence seen during anti-racism protests across the UK at the weekend.
Ms Patel echoed Prime Minister Boris Johnson’s comment that the protests had been “subverted by thuggery” after some demonstrators clashed with police.
She is due to make a statement in the House of Commons later.
Meanwhile, the Voice newspaper’s director Paulette Simpson has called for restraint from protesters.
Anti-racism protests have taken place across the world, following the death of George Floyd, 46, in Minneapolis, in the US, after a white police officer was filmed kneeling on his neck.
Thousands of people attended largely peaceful demonstrations across the UK over the weekend, including London, Manchester and Glasgow.
Unrest in the capital on Sunday led to 35 officers being injured and 36 people being arrested for offences including violent disorder, criminal damage and assaulting police, the Metropolitan Police said on Monday.
Of the officers injured, two required hospital treatment, with one suffering a head wound and the second a shoulder injury after being hit by a thrown bottle.
In Bristol, police are continuing to investigate the “criminal damage” of a bronze statue of Edward Colston – a prominent 17th Century slave trader – which was ripped down by protesters, a move Downing Street called a “criminal act”.
The statue has been a source of controversy in Bristol for years. The city’s mayor said he felt no “sense of loss” at the statue being pulled down.
The PM’s spokesman said Mr Johnson “absolutely understands the strength of feeling” but if people wanted the statue removed, there are “democratic routes” which can be followed.
Mr Johnson does not believe the UK is a racist country but accepts that discrimination is an ongoing issue, the spokesman added.
He said there remains “more to do” and No 10 would not be “complacent” in its efforts to stamp out discrimination and racism “where it happens”.
In Parliament Square in Westminster, a statue of Sir Winston Churchill was sprayed with graffiti and a Black Lives Matter sign attached to it.
Ms Patel told the Daily Mail the “vandals” responsible for the desecration of Churchill’s statue were “repulsive criminals who I want to see brought to justice immediately”.
Met Police Commissioner Dame Cressida Dick condemned the “violent criminality” by a “minority of protesters” as “disgraceful” and said it was “never acceptable” to attack police officers or damage property.
She said given the potential risk of coronavirus being spread at mass gatherings, people should find alternative ways to express their anger and frustration.
Avon and Somerset Police told the BBC 17 people have been identified in connection with the toppling of Colston’s statue. No arrests have yet been made.
Chief Constable Andy Marsh defended the decision taken by commanders on the ground not to intervene when the statue was torn down and dumped in the harbour.
He said arresting suspects could have had “very serious ramifications” for the city of Bristol, including injuries to protesters, police and bystanders.
Labour leader Sir Keir Starmer told LBC radio that the statue should not have been torn down by protesters – but added that it was wrong for the monument to have remained in place for so long.
Ms Simpson, the director of the Voice, one of Britain’s leading black newspapers, said people had a “legitimate right” to protest issues that have “reached boiling point”, but urged people “to restrain themselves” and to try to “contain” their emotions.
She said she did not feel the violence had “hijacked” the protests’ message.
Addressing protesters, she said: “We know that you’re angry, we know that you’re in pain, we know that the you feel there’s no other route to express yourself.”
Ms Simpson questioned why the UK still has statues, symbols and names of streets “that remind us of a very dark place in history”, and urged the government and others to “listen” to those who call for their removal.
It was because of a “lack” of listening and action that “people feel compelled in a pandemic to go and demonstrate,” she added.
John Apter, national chairman of the Police Federation, said while he understood there was “an awful lot of anger and frustration” his “concern and sadness” was that the “legitimate message” of the protests had been “hijacked by some who are intent on violence” against police.
He told BBC Breakfast it was “unforgivable” that some people have been “laughing and joking” about violence faced by police – and warned it could lead many people to “lose sympathy” for the protests.
How George Floyd’s death resonated in the UK
It comes as the head of the Metropolitan Police Federation called on bosses to apologise for failing to protect officers injured in the protests.
Ken Marsh, the chairman of the organisation that represents rank-and-file officers, called for urgent action from Dame Cressida and demanded his colleagues were properly equipped with public order gear, including helmets and shields.
Mr Marsh said police should be dealing with disorder “far more robustly”, adding: “We need to have the correct equipment on to deal with what is in front of us.”
Meanwhile, opposition MPs have criticised comments made by Health Secretary Matt Hancock that the UK protests were fuelled by events in the US “rather than here”.
Shadow justice secretary David Lammy said that racism and prejudice exist in the UK, as well as across the Atlantic, and that to suggest there is only a problem in the US “shows real ignorance”.
Mr Lammy tweeted: “People in this country are not only showing solidarity with George Floyd and other African Americans. We must turn this moment into one of change and justice in the UK too.”
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