Boris Johnson has responded to the Black Lives Matter protests with an article acknowledging the “incontrovertible, undeniable feeling of injustice” motivating the rallies, while condemning those who have flouted social distancing to attend them during a “time of national trial”. The prime minister used the piece in The Voice, and a subsequent video in which he read the text aloud, to set out his response to the protests that saw the statue of slave trader Edward Colston torn down in Bristol and resulted in more than 100 arrests across the UK. “The death of George Floyd took place thousands of miles away – in another country, under another jurisdiction – and yet we simply cannot ignore the depth of emotion that has been triggered by that spectacle, of a black man losing his life at the hands of the police,” Johnson said. “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. “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.” Johnson added: “You are right, we are all right, to say Black Lives Matter; and to all those who have chosen to protest peacefully and who have insisted on social distancing – I say, yes of course I hear you, and I understand. “But I must also say that we are in a time of national trial, when for months this whole country has come together to fight a deadly plague. After such sacrifice, we cannot now let it get out of control.” The home secretary, Priti Patel, has said official estimates suggest 137,500 people have attended the marches. Johnson said BAME communities had “been at the forefront of the struggle against coronavirus – whether in healthcare or transport or social care or any of the other essential services that have kept our country going” – and acknowledged that “it is BAME communities, tragically, that have paid a disproportionate price”. “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 added. He also echoed the insistence of Patel that those involved in what she called “hooliganism” would be brought to justice. “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,” he said. Labour has supported the aims of the protesters, while condemning the minority who resorted to violence. The shadow home secretary, Nick Thomas-Symonds, told MPs on Monday: “I condemn those who have attacked the police, and I want to pay tribute to the police officers putting themselves in harm’s way over the weekend.” • This article was amended on 9 June 2020 to clarify that the 100 arrests made during the Black Lives Matter protests were across the UK, not in Bristol.