Boris Johnson has acknowledged that many of the anti-racism protesters’ concerns are “founded on a cold reality” but has threatened those who harm police or property with “the full force of the law”.

The Prime Minister said the outrage provoked by the death of George Floyd at the hands of a police officer in Minneapolis had awakened an “incontrovertible, undeniable feeling of injustice” and called for people to “work peacefully, lawfully, to defeat racism”.

He said leaders “simply can’t ignore” concerns that black, Asian and minority ethnic (Bame) groups face discrimination in education, employment and criminal law.

But he warned in the wake of campaigners pulling down the statue of slave trader Edward Colston in Bristol and attacks on police that legal repercussions must follow.

And he said he would not support those who break social distancing rules aimed at slowing the spread of coronavirus, which he acknowledged was disproportionately harming Bame communities.

“So no, I will not support those who flout the rules on social distancing, for the obvious reason that we risk a new infection at a critical time and just as we have made huge progress,” he said in a video statement.

“And so I must say clearly that those who attack public property or the police – who injure the police officers who are trying to keep us all safe – those people will face the full force of the law; not just because of the hurt and damage they are causing, but because of the damage they are doing to the cause they claim to represent.

“They are hijacking a peaceful protest and undermining it in the eyes of many who might otherwise be sympathetic.”

As mass protests against the latest killing of a black man at the hands of US police widened to highlight racial inequality more generally, the PM said he understands and hears the anger.

“In this country and around the world his dying words – I can’t breathe – have awakened an anger and a widespread and incontrovertible, undeniable feeling of injustice, a feeling that people from black and minority ethnic groups do face discrimination: in education, in employment, in the application of the criminal law,” he said.

“And we who lead and who govern simply can’t ignore those feelings because in too many cases, I am afraid, they will be founded on a cold reality.”

The statement is Mr Johnson’s fullest comments to date on the Black Lives Matter protests in the UK, with him previously condemning “thuggery” marring demonstrations.

Despite protests including in London and Bristol largely being peaceful, nearly 50 officers were injured over the weekend and graffiti was also scrawled on a statue of Sir Winston Churchill in Parliament Square.

Labour leader Sir Keir Starmer said it was “completely wrong” for protesters to rip down the Colston statue and toss it into the harbour, but told LBC Radio the monument to the slaver should have been removed long ago.

Bristol Mayor Marvin Rees said he felt no sense of loss for the statue, but told BBC Radio 4’s Today programme: “As an elected politician, obviously I cannot condone the damage and I am very concerned about the implications of a mass gathering on the possibility of a second Covid wave.”

Mr Johnson said the UK has “made huge strides” in confronting racism but said “there is so much more to do”.

He also praised his own record, citing work “to recruit and promote more young black people” and noted his Chancellor, Rishi Sunak, and Home Secretary, Priti Patel, are of Indian heritage.

But protesters have also directed criticism at the PM, particularly for his past writings for which he has himself been accused of racism.