The protests, sparked by the death of George Floyd in the US, were 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 majority of the day's protests were peaceful but in the evening there were disturbances outside Downing Street.
BBC home affairs correspondent Tom Symonds said the protest was largely over when missiles and fireworks were thrown at a police line.
Police horses were used to regain control, but one horse galloped ahead and its rider fell to the ground after hitting her head on a traffic light. Her injuries are not life-threatening, the Metropolitan Police said.
Fourteen people were arrested and 10 officers were injured after a smaller group became "angry and intent on violence", the force added.
In a tweet, Mayor of London Sadiq Khan told the protesters "I stand with you and I share your anger and your pain" and said the small minority of people who became violent "let down this important cause".
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".
