UK chief constables have said they stand alongside all those “appalled and horrified” by the way African-American George Floyd died in US police custody.
In a joint statement, they said the right to lawful protest was a “key part of any democracy” but stressed coronavirus remains a “deadly disease”.
The police leaders said restrictions remained, including not gathering outside in groups of more than six.
The warning comes as hundreds protest around the UK.
Protests began in the US after a video showed Mr Floyd being arrested on 25 May in Minneapolis and a white police officer continuing to kneel on his neck even after he pleaded that he could not breathe.
The officer, Derek Chauvin, has been charged with third-degree murder.
Prime Minister Boris Johnson said on Wednesday that Mr Floyd’s death had been “appalling” and “inexcusable”, but was criticised for failing to comment on the killing before now.
SNP Westminster Leader Ian Blackford said the UK government had “shuttered itself in the hope no-one would notice”.
Meanwhile, Labour leader Sir Keir Starmer called on the PM to convey to US President Donald Trump the UK’s “abhorrence about his response to the events”.
In the US, tens of thousands of people demonstrated for an eighth night, mainly peacefully.
The Floyd case has reignited deep-seated anger over police killings of black Americans and racism.
Demonstrators have taken to the streets – not only to express their outrage at the treatment of Mr Floyd – but to condemn police brutality against black Americans more widely.
In the UK, hundreds of people have gathered in London’s Hyde Park for a protest organised by campaign group, Black Lives Matter.
Organisers asked people to spread their arms out to maintain a two-metre distance from each other, as crowds chanted “the UK is not innocent”.
One activist attending the protest, Brogan Baptiste, told the BBC earlier: “It’s imperative that all of us, whether you’re black, white, that you’re involved in this because we need change and we need it now.”
Filippa, a 20-year-old student who also joined the protest, said: “I know that I’m healthy. So this felt more important than to stay inside when I have the opportunity.”
In their joint statement, the National Police Chiefs Council said: “We stand alongside all those across the globe who are appalled and horrified by the way George Floyd lost his life. Justice and accountability should follow.
“In the UK, we have a long-established tradition of policing by consent, working in communities to prevent crime and solve problems.
“Officers are trained to use force proportionately, lawfully and only when absolutely necessary,” the statement continued.
“We strive to continuously learn and improve. We will tackle bias, racism or discrimination wherever we find it.”
The police leaders added that “sometimes we fall short” but “when we do, we are not afraid to shine a light on injustices or to be held to account”.
They said UK police “uphold and facilitate” the right to lawful protest and “we know people want to make their voices heard”.
However, amid the coronavirus pandemic they stressed restrictions on gatherings were still in place and urged people to “continue to work with officers at this challenging time.”
Meanwhile, campaign group Stand Up to Racism (SUTR) is urging Britons to “take the knee” on their doorsteps for a socially-distanced protest at 18:00 BST.
SUTR said the campaign was inspired by the kneeling protest staged by American football star Colin Kaepernick in 2016 that has become synonymous with the Black Lives Matter movement.
On Tuesday evening, civic buildings in cities including London, Liverpool and Cardiff turned purple to honour Mr Floyd’s memory, with other cities around the country promising similar tributes on Wednesday evening.