Video report by ITV News Correspondent John Ray
The Prime Minister has condemned "racist thuggery" following a day of violent clashes between police and far-right protesters.
Police in London struggled to contain the group which had gathered on Parliament Square, claiming they were there to protect statues.
Officers were pelted with bottles during confrontations and were forced to disperse protesters who remained past a 5pm curfew that had been announced in advance.
Six officers suffered minor injuries after "pockets of violence" were directed towards the Metropolitan Police, the force said.
It added more than 100 people had been arrested during the protests, for offences such as violent disorder, assault on officers, and drunk and disorder.
Boris Johnson tweeted: "Racist thuggery has no place on our streets.
"Anyone attacking the police will be met with full force of the law. These marches & protests have been subverted by violence and breach current guidelines.
"Racism has no part in the UK and we must work together to make that a reality."
Many of those present were drinking and there were a number of clashes with police in riot gear - crowds were heard chanting "England" and raising their arms.
Similar demonstrations took place around the country, with hundreds gathering around the Cenotaph in Bristol and clashes between police and protesters in Newcastle city centre.
Commenting on the day's events, Home Secretary Priti Patel said: "We live in a tolerant country but racism, any form of intolerance and violence is simply not acceptable."
She added: "We have seen a small minority behave in extreme thuggery and violent behaviour today.
"That is simply unacceptable and the individuals that are basically putting the safety of our police officers and the safety of the public at risk will expect to face the full force of the law."
Following the conclusion of the protest on Saturday, Met Commander Bas Javid said: "Thousands have travelled to London despite being asked not to and some of those have been intent on causing harm.
"We understand why people want to express their concerns and have worked hard to keep people safe.
"Many people have complied with these conditions, and have listened to officers during the day, and have behaved as we have requested in order to keep them safe.
He added, however: "A number of people have not followed these conditions, putting officers, and others’ safety at risk.
"There have been pockets of violence directed towards our officers. This is completely unacceptable and I condemn those involved."
At one point, police intervened to stop the far-right gathering approaching Hyde Park where a Black Lives Matter demonstration, which had largely been peaceful, was taking place.
Hundreds of mostly white men converged in central London earlier on Saturday after far-right groups, including Britain First, called on supporters to guard the monuments amid Black Lives Matter protests.
Several hundred demonstrators blocked roads around Parliament Square, while police tried to corral them onto the pavements.
Other officers, some holding shields, remained in a line blocking access to the Cenotaph in Whitehall, while some in the crowd screamed abuse at them.
Police blocked off all the exits to the square for a time on Saturday, causing demonstrators to jump a fence into the grounds of Westminster Abbey in order to leave.
Meanwhile police say they are investigating a man taking part in far-right protests who urinated next to a memorial to Pc Keith Palmer in Westminster.
Tobias Ellwood, the Tory MP and chairman of the Defence Select Committee who gave first aid to the dying police officer at the time of the attack, wrote on Twitter: "Absolute shame on this man.
"Of all the images to emerge over these few testing days I find this one of most abhorrent.
Senior Conservative MP and Father of the House of Commons, Sir Peter Bottomley, said the protester should be "ashamed".
Labour’s shadow home secretary Nick Thomas-Symonds said he was “extremely disturbed” by the “completely unacceptable” scenes of violence on the streets following protests on Saturday.
“I want to say a particular word as well about that awful scene of someone urinating next to PC Keith Palmer’s memorial," Mr Thomas Symonds told Sky News’ Sophy Ridge.
“Absolutely despicable behaviour and I hope that individual is identified and brought to justice.”
Mr Thomas-Symonds said he also would back the Government in creating a specific offence against damaging war memorials and said he would be willing to work cross-party to support such efforts in Parliament.
While Metropolitan Police Federation chairman Ken Marsh said the man pictured should be sent to prison.
Mayor of London Sadiq Khan also condemned the violence, writing:
"This is totally unacceptable. We will not tolerate attacks on our police and perpetrators will feel the full force of the law.
"It is clear that far right groups are causing violence and disorder in central London, I urge people to stay away."
Aerial footage shows clashes between protesters and police. This footage has no sound
Protesters say the action was triggered after statues in Parliament Square including of Winston Churchill, Nelson Mandela and Mahatma Gandhi, were boarded up on Friday.
The statues of Mandela and Gandhi were again targeted on Saturday, as police on horseback tried to push demonstrators back while protesters continued to throw objects towards them, including at least one smoke bomb.
The large group of far-right protesters then moved to Trafalgar Square, where fireworks were thrown across the crowds.
The violence continued as 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.
Speaking before the clashes, Paul Golding, leader of Britain First, said the crowds had turned out to "guard our monuments".
He told thePA news agency: "I am extremely fed up with the way that the authorities have allowed two consecutive weekends of vandalism against our national monuments.
"Anyone who comes along today to try and vandalise them will probably be dealt with by all of these Englishmen that turned up, and they’re fed up as well."
In response to the statements by far right groups ahead of a planned event on Saturday, Black Lives Matter organisers urged supporters to stay away from central London.
The group held a demonstration in London on Friday while some protesters gathered in Hyde Park on Saturday.