In the early hours of Saturday morning, as thousands of people gathered along the Coronation Route of the procession, the police arrested several members of the anti-monarchist group.
The arrests were considered a controversial move as the protesters were not actually protesting when the police arrived.
He metropolitan police it has now said that an investigation could not prove that the protesters intended to disrupt the event.
In a statement, police said they regretted the decision to arrest them and that no further action would be taken.
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They added: “Tonight all six had their bail canceled and no more will be taken.
“We regret that those six people arrested have not been able to join the wider group of protesters in Trafalgar Square and elsewhere on the procession route.”
The leader of Republic, and one of those arrested, Graham Smith, said he confirmed that the arrested Republic protesters have been told no charges will be brought against them.
Smith also called for a full investigation into who authorized the arrests during what he described as an “embarrassing episode.”
Mr Smith added: “The speed with which they did this shows that they realized very quickly that they had made a very serious error in judgment and action will be taken again. Advertisement
“Obviously I’m relieved that they left so quickly, but very angry that they even took this path, robbing people of their freedom for no reason. There was no evidence of any ability or intent to commit any crime and they just decided to arrest us and that’s outrageous.”
Smith said a chief inspector and two other Met officials apologized to him in person at his home Monday night.
He said: “I had three officers at my door apologizing personally and giving me the straps back. They were a chief inspector and two other officials from the Met.
“They seemed pretty embarrassed, to be honest. I said for the record that I will not accept the apology. We have many questions to answer and we will take action.”
In total, the agents arrested 64 people on the day of the Coronationwith 46 of them released on bail after being detained on suspicion of causing a public nuisance or disturbing the peace.
Following the arrests, police were charged with an alarming attack on protest rights in the UK. Culture Secretary Lucy Frazer said BBCOn Sunday with Laura Kuenssberg that the police were right to take into account the scale and global nature of the event.
Ms Frazer said: “We were on the global stage, there were 200 foreign dignitaries in the UK, in London at an event, millions of people watching and hundreds of thousands of people on the scene.”
The arrest of the Republic protesters came just days after new legislation was introduced into the Public Order Act making it illegal to prepare to blockade.
The new laws also mean that protesters who block roads, railways or airports could face up to a year in jail.
Additionally, anyone who blocks objects, others, or other buildings could face six months behind bars or an unlimited fine.
Critics say one of the most troubling new laws allows police to stop and search protesters if they suspect they are causing a disturbance.
Liberty Police and Campaigns Officer Jun Pang said the Guardian: “It is worrying to see the police handed out so many new powers to restrict protests, especially before a big national event.
“When the Police, Crime, Sentencing and Courts Act came into force, they were repeatedly abused by the police, partly because they simply did not understand them.
“Similarly, when Queen Elizabeth died, we saw the police acting inappropriately and with a heavy hand towards the protesters who violated their rights.”