The protests, sparked by the death of George Floyd in the US, are being held in cities including London, Manchester, Cardiff, Leicester and Sheffield.
In London, protesters knelt for a minute's silence before chanting "no justice, no peace" and "black lives matter".
The protests went ahead despite officials advising against mass gatherings due to coronavirus.
Home Secretary Priti Patel said the social distancing advice was "for the safety of all of us", while Met Police Commissioner Dame Cressida Dick said the protests were "unlawful".
The vast majority of the day's protests were peaceful.
But later in the evening, as demonstrators dispersed in London, there were disturbances outside Downing Street.
Earlier thousands of people gathered in the capital, the majority donning face coverings and many with gloves.
Some held signs making reference to coronavirus, including one which read: "There is a virus greater than Covid-19 and it's called racism".
Meanwhile, in Northern Ireland, police said they had issued "a significant number" of fines given the dangers of crowds in the pandemic.
Protests began in the US after a video emerged of Mr Floyd, a 46-year-old black man, being arrested by four officers on 25 May in Minneapolis.
Videos showed Mr Floyd, who was unarmed and in handcuffs, dying after a white policeman knelt on his neck for nearly nine minutes. The footage - seen all around the world - showed him gasping that he could not breathe.
An officer has been charged with murder while three of his colleagues stand accused of aiding and abetting the killing.
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