The protesters did not observe social distance and most of them were without masks, so the police demanded them to leave the square.
Officers removed sound equipment and penned the crowd in Trafalgar Square as water and bottles were thrown at them by demonstrators - with some chanting "pick your side".
Police used batons against protesters, leaving some with visible injuries.
According to the city police, at least three protesters and nine officers were injured, and 16 people were detained.
London Mayor Sadiq Khan said: "The reckless and violent behavior of some protesters has left hard-working police officers injured and put the safety of our city, which is at a critical moment in the fight against this virus, at risk. This is totally unacceptable."
"Violence of this kind towards officers will not be tolerated and perpetrators will feel the full force of the law."
According to Worldometers, since the beginning of the pandemic in the UK, 429, 277 people have got infected with Covid-19, for 41,971 of them the disease turned out to be fatal.
As reported earlier, a protest action took place under the walls of the Chernivtsi regional state administration. Chernivtsi City Council prepared a lawsuit against the government's decision according to which the city was assigned to the "red" quarantine zone.