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