Video footage shared by journalists at the scene shows protesters clashing with mounted police in front of a boarded-up statue of Nelson Mandela and shouting at officers just metres from the Cenotaph.
The Metropolitan Police said six officers had suffered minor injuries after “pockets of violence” during the protests.
Boris Johnson said anyone attacking the police “will be met with the full force of the law”.
“Racist thuggery has no place on our streets,” the prime minister tweeted.
“These marches and protests have been subverted by violence and breach current guidelines.”
Scotland Yard said that, as of 5pm, they had arrested five people for offences including violent disorder, assault on police, possession of an offensive weapon, being drunk and disorderly and possession of Class A drugs.
Anti-racism protests were due to gather in Hyde Park at 1pm today, but were called off after Sadiq Khan warned Black Lives Matter organisers that far-right groups, including Britain First and the Democratic Football Lads Alliance were planning to hijack the rally.
The Metropolitan Police imposed a number of conditions on the protests, including telling attendees that they must disperse by 5pm on Saturday.
At around 1pm police on horseback were seen pushing demonstrators back from the other end of Parliament Square, near the boarded-up statues of Nelson Mandela and Gandhi.
Several bottles, including a large vodka bottle, and cans were thrown at the officers, with a device emitting dark smoke into the crowd. Some of the demonstrators were also seen blocking others in their group from the police horses.
Crowds could also be seen running through Trafalgar Square, while protesters reportedly threw fireworks at police officers during violent clashes in the city centre.
Other protesters gathered near the Cenotaph, and could be heard chanting Lee Rigby’s name – despite the murdered soldier’s family urging people not to use his name or image to counter Black Lives Matter protests.
A demonstrator from South London, who gave her name as Victoria, was in the square with a banner reading “All lives matter”.
Discussing controversial statues, she told PA: “It’s the past. You’ve just gotta learn to live with it, they’ve done what they’ve done but it’s still in the records they did good things.
“I’ve got things I don’t want to remember, but I wouldn’t go smashing things up because of it.”
Daisy, a 26-year-old from Pimlico, passed demonstrators in Parliament Square as she went for a run at around 10.30 on Saturday morning and claimed many were already drinking alcohol.
“They were all drinking beers and there was already loads of cans lying round on the floor treating it like it was some sort of football away-day,” she told PA.
“It was a really tense and hostile atmosphere. I didn’t stay too long… it was really uncomfortable.”
As the scene became more hostile, home secretary Priti Patel tweeted: “[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.”
There were similar protests in other parts of the country.
Several dozen people, many of them clad in motorcycle gear, met in front of the Cenotaph in Bristol on Saturday morning just metres away from where slaver Edward Colston’s statue stood before it was torn down during a Black Lives Matter rally on Sunday.
They were later joined by several hundred demonstrators who were filmed pulling up placards at the base of the Colston plinth and stuffing them into a bin bag.
Vans were filmed delivery pallets of beer to attendees, and several men climbed onto the platform where the Colston statue once stood, with one holding a Union Jack up in in front of the crowd.
Several hundred people also gathered outside City Hall in Belfast in Northern Ireland to protect war memorials.
The Northern Ireland Cenotaph Protection Group (NICPG) issued a statement saying its aim is to protect war memorials amid attacks on statues of historical figures across the UK in recent days.
“We are not a counter protest, we do not have a political message. For those of us who served we served beside men and women of all cultural backgrounds, and those veterans that have been in combat know, above all else, regardless of what colour you are, we all bleed red,” it said.
Several demonstrators wore British military uniforms while Union flags and Ulster flags were draped over the railings of City Hall.
While most demonstrators wore masks there was a lack of social distancing.
Officers from the Police Service of Northern Ireland attended the demonstration.
Hundreds of people also flocked to George Square in Glasgow to “protect” a war memorial.
In an event organised by a group called the Loyalist Defence League (LDL), people congregated to stop vandalism to the Glasgow Cenotaph, erected to commemorate the lives of those who died in the First World War.
The group was penned in on the east side of the square, with a similar sized area reserved for counter-protesters which remained empty.