The Met Police says officers on duty on Armistice Day were met with "violence and abuse". Bottles and other missiles were thrown at officers by what the force referred to as "counter protesters".
Videos show men, some draped in Union Jacks and St George's Flags, shouting "you're not English anymore".
A two-minute silence was observed at the Cenotaph without incident.
A large pro-Palestine rally has taken place elsewhere in London today, after Met commissioner Sir Mark Rowley resisted calls to institute a ban.
Far-right groups have taken to the streets in a "counter protest".
The Met Police said at 2.45pm: "Officers have arrested 82 people in Tachbrook Street, Pimlico to prevent a breach of the peace.
"They’re part of a large group of counter protestors we have been monitoring who have tried to reach the main protest march. We will continue to take action to avoid the disorder that would likely take place if that happened."
The force added: "In addition to the arrests made to prevent a breach of the peace in Tachbrook Street, we have made 10 arrests today for other offences. These include possession of offensive weapons, affray and possession of drugs."
Dispersal zones were put in place to support policing over the weekend.
The large pro-Palestine march to the American embassy began from Hyde Park, well away from the Cenotaph and Armistice ceremonies.
"There have been no incidents related to this protest so far," said the Met at just after 1pm.
The home secretary this week came under criticism for an article in the Times in which she accused the Met Police of treating the policing of right-wing protests differently to pro-Palestinain demonstrations.
She previously referred to protest marches which have taken place weekly since the Hamas terrorist attacks and Israel's response in Gaza as "hate marches". Along with prime minister Rishi Sunak, she called for this week's protest to be banned.
Met Police commissioner Sir Mark Rowley said there was no justification for such a ban. Organisers of the march have been in conversation with the Met and the event was never going to take place near the Cenotaph.
Ms Braverman has been accused of risking emboldening right-wing groups.
Mayor London Sadiq Khan said: "The scenes of disorder we witnessed by the far-right at the Cenotaph are a direct result of the Home Secretary’s words. The police's job has been made much harder.
"The Met have my full support to take action against anyone found spreading hate and breaking the law."
Scotland's first minister, Humza Yousaf, post on X: "The far-right has been emboldened by the Home Secretary. She has spent her week fanning the flames of division. They are now attacking the Police on Armistice Day.
"The Home Secretary's position is untenable. She must resign."
Armistice Day two minute silence
Hundreds of people gathered in Whitehall near the Cenotaph on Saturday morning.
At 11am a two-minute silence marked the Armistice.
It was observed without interruption, save for the birds in the trees and a helicopter overhead.
Pro-Palestine protest - 'very large turnout'
The protest march was scheduled to begin in Hyde Park at midday.
The Met Police said: "The pro-Palestinian demonstration has set off from Park Lane. As expected there is a very large turnout.
"There have been no incidents related to this protest so far. The significant policing operation is continuing and we’ll post any relevant updates here."