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Rishi Sunak has condemned "violent, wholly unacceptable" actions by far-right groups and "Hamas sympathisers" after protests and clashes in London.
About 300,000 pro-Palestinian protesters marched to call for a ceasefire, in the biggest UK rally since the Israel-Gaza war began.
Counter-protesters made up the "vast majority" of the 126 arrests, police said.
Most were to "prevent a breach of the peace".
Clashes were reported by police at London's Cenotaph and in Chinatown.
The prime minister condemned "violent, wholly unacceptable" actions by far-right groups and "Hamas sympathisers".
"All criminality must be met with the full and swift force of the law," he said in a statement posted on X, formerly Twitter.
Scuffles first broke out shortly after 10:00 GMT as police attempted to stop a crowd of people carrying St George's flags marching along Embankment towards Whitehall where the Cenotaph - the 103-year-old war memorial - is located.
Officers faced aggression from some of the counter-protesters - who include some far-right groups - near the Cenotaph, the Metropolitan Police said.
The group, which had been chanting "England 'til I die" pushed through the police barrier, with some shouting "let's have them".
However, a two-minute silence held at the Cenotaph at 11:00 GMT to mark Armistice Day was observed "respectfully", police added.
A video, shared by the Met on X showed another clash, with counter-protesters shoving police officers and chanting: "You're not English, you're not English, you're not English any more." Police said a group who had moved into Chinatown "confronted and threw missiles at officers who tried to engage with them".
More than 80 counter-protesters who "tried to reach the main protest march" were arrested to "prevent a breach of the peace", police said.
Ten others were arrested for other offences including possession of offensive weapons, affray, and possession of drugs.
Scotland Yard said many of the counter-protesters arrested were connected to football hooliganism, and some of them had previous convictions for football violence.
During the protests, BBC News was given rare access to the Met Police's control room in south London, which has access to thousands of cameras.
One live feed from a police helicopter was powerful enough to show a man sitting in a pub window and how much he had left in his drink.
On the pro-Palestinian march, chants of "free Palestine" and "ceasefire now" could be heard as crowds began marching from London's Hyde Park.
At one point the march, organised by the Palestine Solidarity Campaign, extended from the Hilton Hotel in Park Lane to the US Embassy in Nine Elms - a distance of roughly 2.5 miles. Organisers believe 800,000 people attended but police estimated 300,000.
One demonstrator told BBC News: "We want a ceasefire. People are suffering, children are dying under the rubble, and no one seems to care about them."
He also criticised the prime minister for saying the timing of the march was disrespectful as it coincided with Armistice Day. The man added: "It is disrespectful to allow children to die."
Another protester said: "I think it is the perfect day to actually do it on. Because that's what armistice is, it is a call for ceasefire and a call for stopping war."
Elsewhere, footage shared on social media showed Michael Gove ushered through London's Victoria Station by police officers as crowds waving Palestinian flags shouted: "Shame on you."
A source close to the levelling up secretary said he had been returning from his constituency and was taken away in a police van.
In his statement, Mr Sunak said: "I condemn the violent, wholly unacceptable scenes we have seen today from the EDL and associated groups and Hamas sympathisers attending the National March for Palestine.
"The despicable actions of a minority of people undermine those who have chosen to express their views peacefully."
He said the clashes "utterly disrespects" the honour of "our Armed Forces", saying "that is true for EDL thugs attacking police officers and trespassing on the Cenotaph" and also for "those singing antisemitic chants and brandishing pro-Hamas signs and clothing on today's protest".
Assistant Commissioner Matt Twist said hundreds of counter-protest demonstrators had "seemed intent on confrontation and intent on violence".
In a statement, he praised his officers - "who put themselves in harm's way" - for ensuring "nobody was able to reach the Cenotaph, which was protected at all times".
He added: "Locating and intercepting suspects in a crowd of the size we saw today will always be challenging, but we were further limited in our ability to do so due to the number of officers we had to deploy, from early in the day, in response to violence from the right wing groups in central London."
The Met have issued photos of three individuals it suspects of antisemitic hate crimes during the protest.
One shows a woman carrying a placard on which the Jewish symbol, the star of David, is shown to incorporate a Swastika.
Two other men are shown in photographs taken apparently during the march.
No major protest is scheduled to take place on Remembrance Sunday, although the policing operation will continue with some 1,375 officers deployed amid commemoration events in the capital.
The Met said it had made 188 hate crime arrests - the majority for antisemitic offences - since the conflict between Hamas and Israel erupted on 7 October.