Police were pelted with bottles during confrontations with demonstrators in London, where hundreds gathered despite warnings to avoid protests.
Groups gathered in the centre of the capital, claiming they were protecting statues from anti-racism activists.
Home Secretary Priti Patel described the violence as “thoroughly unacceptable thuggery”.
Some anti-racism demonstrations have also taken place across the UK, including in central London.
The Met Police had placed restrictions on several groups intending to protest, following violent scenes last weekend.
Various groups from around the country, including right-wing activists, said they had come to London to protect symbols of British history.
Hundreds of mostly white men gathered around the Cenotaph war memorial in Whitehall and the boarded-up statue of Winston Churchill in Parliament Square.
There were a number of clashes with police in riot gear as crowds – chanting “England” and raising their arms – surged towards lines of officers.
Some protesters managed to break metal barriers around the Cenotaph on Whitehall while hurling flag poles, a smoke flare and a traffic cone towards police who were striking them back with batons.
Large groups of far-right protesters then moved to Trafalgar Square, where fireworks were thrown across the crowds.