The offenses as of 9 p.m. included violent disorder, assault on officers, possession of an offensive weapon, possession of class A drugs, and drunken disorder, London's Metropolitan Police said in a tweet.
Far-right groups bombarded police with bottles and occasionally scuffled violently with officers as they staged a counter-protest in central London.
Police also arrested a 28-year-old man after an individual was photographed on Saturday apparently urinating on a memorial to a police officer killed while defending Parliament from a terrorist attack in 2017.
The man was arrested north of London "on suspicion of outraging public decency," police said.
Hundreds of mostly middle-aged white men, many shirtless or clutching beers, gathered in Parliament Square, where video showed a small number of right-wing protesters throwing objects at a line of police, some of whom responded with batons.
The groups, some of them chanting "England" during clashes, said the counter-protest was intended to "protect" statues around Parliament Square, including that of wartime prime minister Winston Churchill.
UK Home Secretary Priti Patel described the behavior as "thoroughly unacceptable thuggery."
"Any perpetrators of violence or vandalism should expect to face the full force of the law. Violence towards our police officers will not be tolerated. Coronavirus remains a threat to us all. Go home to stop the spread of this virus & save lives," she said.
In Trafalgar Square, officers formed barriers between BLM and far-right groups, as authorities in the UK capital urged people to stay away from the protests, given the high likelihood of violence.
The statue of Churchill was boarded up, as were statues of Nelson Mandela and Mahatma Gandhi. One self-declared England fan and soccer hooligan confirmed to CNN last week that there were threats to pull down the Mandela statue.
The Mayor of London's office said: "The statues of Winston Churchill, Nelson Mandela and Mahatma Gandhi are being temporarily covered for their protection. All other statues in Parliament Square and Trafalgar Square remain under review and we will put protection in place should the need arise."
London's Metropolitan Police imposed a 5 p.m. (12 p.m. ET) limit on both the Black Lives Matter and right-wing protests in the UK's capital. They also imposed conditions on what route and area the protesters could use, to try to prevent the two groups clashing. Protests planned by Black Lives Matter and associated groups were to follow a planned route from Hyde Park to Trafalgar Square while protests by right-wing groups were to stay in Parliament Square and Whitehall, south of a police barrier.
In a statement released Friday, Met Police Commander Bas Javid said: "I absolutely understand why people want to make their voices heard -- there is a really strong depth of feeling out in the communities, but the Government direction is that we remain in a health pandemic and people are asked not to gather in large groups. By doing so, you are putting your own safety, and that of your family or friends at risk. We are asking you not to come to London, and let your voices be heard in other ways."
CNN has previously reported comments from Metropolitan Police Commissioner, Cressida Dick, that her forces had information that people were "intent on coming to cause violence and confrontation" at BLM marches across London this weekend.
"We can anticipate that some of them, whatever their political persuasion, are intent, some of them, are intent on having a confrontation with people from the Black Lives Matter movement. So my message is please just stay away this weekend," she said.
The UK's official Black Lives Matter group distanced itself from the protest that it had planned in central London on Saturday. "Please, people, our people, if you want to protest this weekend, do it in your ends," it tweeted, adding, "Our priority must be our safety -- please take care of yourselves and each other."
UK anti-racism charity Hope Not Hate had warned about the possibility of violence from "football hooligans" and far-right groups at protests this weekend. "While the hooligan