I think it's important to be clear that the police have not been arresting protestors "for being anti-monarchy in public". While calling for the abolition of the monarchy is technically illegal under section 3 of the Treason Felony Act 1848, a prosecution has not been brought since 1879. For example, when the King was presented with the Scottish regalia at Edinburgh on July 5th, there were "hundreds of peaceful protestors" according to Police Scotland, and just four eventual arrests - one for theft, one for an existing warrant, and two for a breach of the peace after allegedly climbing over a safety barrier. This last offence is presumably referring to an alleged breach of section 38 of the Criminal Justice and Licensing (Scotland) Act 2010.
At the coronation of King Charles in May 2023, there were 64 arrests, according to the Metropolitan police, for a number of alleged offenses:
52 of these related to concerns people were going to disrupt the event, and arrests included to prevent a breach of the peace and conspiracy to cause a public nuisance. As part of the wider policing operation eight arrests were made for other offences, including possession of an offensive weapon, drugs offences, and breaching a sexual harm prevention order.
The press release goes on to mention the arrest of six individuals on suspicion of going equipped for locking on (for example, supergluing or zip tieing themselves to street furniture), contrary to Section 2 of the Public Order Act 2023. After investigating the items seized from the individuals, the police released them, cancelled their bail, and apologised:
The investigation team have now fully examined the items seized and reviewed the full circumstances of the arrest. Those arrested stated the items would be used to secure their placards, and the investigation has been unable to prove intent to use them to lock on and disrupt the event. This evening all six have had their bail cancelled and no further action will be taken. We regret that those six people arrested were unable to join the wider group of protesters in Trafalgar Square and elsewhere on the procession route.
There have been a few other arrests, for example a man arrested on suspicion of threatening behaviour after throwing eggs at the King, contrary to section 4 of the Public Order Act 1986. He was eventually sentenced to a 12-month community order and 100 hours of unpaid work. I'm sure I've missed some, so please leave a comment if you have any more specific examples you'd like me to add.
The policing of the coronation in particular was examined in Parliament by the Home Affairs Select Committee on May 17th, and a transcript of the oral evidence heard may be found on their website. The committee heard from the Metropolitan Police, the National Police Chiefs' Council, the anti-monarchy group Republic, and others. The Assistant Commissioner of the Met, Matt Twist, was asked whether the police had had due regard to their duty under section 6 of the Human Rights Act to facilitate protest, for example:
Of course, and I have seen reporting, which is completely erroneous
and false, that suggests that all protest was prohibited, banned or in
some way constrained. That simply is not the case. We are very
familiar with our duties around dealing with protest, both positive
duties under the Human Rights Act and negative duties. Balancing the
rights of people who wish to protest with those impacted by the
protest is part of the day-to-day job of policing in London.
At a later session, the Home Secretary supported the policing efforts, and told the committee that the event "was a success for the police. It went off unimpeded, and people were able to enjoy that historic event."
An urgent question was also tabled in the House of Commons by SNP MP Joanna Cherry, and answered by Chris Philp, the Minister for Crime, Policing, and Fire:
Today, Commissioner Mark Rowley has outlined the intelligence picture
in the hours leading up to the coronation. It included more than one
plot to cause severe disruption by placing activated rape alarms in
the path of horses to induce a stampede and a separate plot to douse
participants in the procession with paint. That was the context: a
once in a generation national moment facing specific intelligence
threats about multiple, well-organised plots to disrupt it. The focus
of the police was, rightly, on ensuring that the momentous occasion
passed safely and without major disruption. That was successful. All
plots to disrupt the coronation were foiled by a combination of
intelligence work and proactive vigilant policing on the ground. I
would like to thank the police and congratulate them on that success.
At the same time, extensive—[Interruption.] Wait for it. At the same
time, extensive planning ensured that protests could take place. That
was also successful. Hundreds of protesters exercised their right to
peaceful protest, including a large group numbering in the hundreds in
and around Trafalgar Square. Where the police reasonably believed they
had grounds for arrest, they acted. The latest information is that 64
arrests were made. I will not comment on individual cases or specific
decisions, but the arrests included a person wanted for sexual
offences, people equipped to commit criminal damage with large
quantities of paint, and arrests on suspicion of conspiracy to cause
public nuisance, often backed by intelligence. The Met’s update last
night included regret—to use its word—that six people arrested could
not join the hundreds protesting in Trafalgar Square and nearby. The
Met confirmed that those six people have now had their bail cancelled
with no further action.
His full statements and the full debate may be found in Hansard.