Civil liberties campaigners and others have expressed alarm about the response of police to anti-monarchy protesters after a number of incidents, the latest of which included the arrest of a man in Edinburgh for apparently heckling Prince Andrew.

The advocacy group Liberty said that new powers recently given to the police to curtail protest, and how they were being enforced by officers, were a cause for deep concern.

The Labour MP Zarah Sultana said in response to incidents in Edinburgh, London and Oxford: “No one should be arrested for just expressing republican views. Extraordinary – and shocking – that this needs saying.”

Police Scotland said a 22-year-old man and a 52-year-old man had been arrested in connection with a breach of the peace on the Royal Mile in Edinburgh shortly before 3pm on Monday.

It came after police were seen pulling a man out of a crowd of people, some of whom appeared to push him, after he was seen shouting at the procession accompanying the Queen’s coffin as King Charles, the Princess Royal, the Duke of York and the Earl of Wessex marched behind the hearse.

Earlier, a woman was charged after being arrested by police in Edinburgh on Sunday as she staged a protest during the accession proclamation for the King. Police said the woman, 22, had been arrested on Sunday outside St Giles’ Cathedral in connection with a breach of the peace and would appear at Edinburgh sheriff court at a later date.

The woman, called Mariángela and who had been seen holding a sign that said “Fuck imperialism, abolish monarchy”, was arrested moments before the reading of the proclamation. The incident took place outside the cathedral, where the Queen’s coffin lay on Monday.

On Monday night Global Majority Vs Campaign, the group Mariángela represents, released a statement following the arrest, saying it “condemned the centuries of colonial injustice, genocide, and unlawful extraction that have been – and continue to be – carried out in the name of the British Crown”.

It added: “Calling for the abolition of the monarchy is as old as the monarchy itself and a cornerstone of freedom of speech in the UK.”

In London, a barrister and climate activist who had held up a blank piece of paper in Parliament Square said he had been threatened with arrest by a police officer under the Public Order Act.

“He confirmed that if I wrote, ‘Not My King’ on it, he would arrest me under the Public Order Act because someone might be offended,” the lawyer, Paul Powlesland, said on Twitter.

“A period of quiet mourning for the Queen is fine, but using that period to cement Charles’ accession as King and cracking down on any dissent to the accession as disrespectful is outrageous.”

Powlesland told the Guardian on Monday night that he had had quite a long discussion with the police who had stopped him, who were from Norfolk’s force. “I speak in a certain way, was dressed in a certain way and understood the law, but someone else might have been in a different situation,” he said.

“Normally, you can get into trouble for shouting, but if you have something written that is super-factual and which is not abusive, then you would normally think that you are protected. It’s pure free speech.”

“I think the idea that he could arrest me and that there could be a conviction under the Public Order Act was ludicrous, but interventions like that are having a chilling effect,” Powlesland added. “I didn’t hold up the sign in the end because I have to work tomorrow and could not afford to be detained. A lot of other people might simply be chilled into not protesting.”

Powlesland tweeted a video recording of an exchange that he appeared to have had with the officer, who could be heard telling him that someone might be offended if the lawyer were to write, “Not my king” on the piece of paper he was carrying.

Jodie Beck, policy and campaigns officer at Liberty, identified an incident in Oxford on Sunday in which a man was arrested on suspicion of a public order offence, under section 5 of the Public Order Act 1986.

Thames Valley police said they had subsequently de-arrested Symon Hill, who said he had been arrested for shouting, “Who elected him?” when the proclamation of the new king was read out in Oxford.

Hill, 45, said he had come across the event by chance as he walked home from church. The history tutor said that after he shouted the words, some people nearby told him to “shut up” and he responded by saying: “A head of state has been imposed on us without our consent.”

Beck said: “The number of cases we have seen in the last couple of days comes at a time when the police have just been given a bunch of new powers, which range from being able to impose conditions on public assemblies and moving protests or act in the case of other gatherings which are viewed to have created lots of noise.

“Given the context we are in at the moment and where the landscape for protest is really being shrunk continually, it’s not surprising that the police are interpreting certain pieces of legislation in a completely warped way.” She added that the police also had a duty to facilitate protest.

The Metropolitan Police on Monday night appeared to acknowledge the reaction to Powlesland’s tweets after they had gone viral, issuing a statement it was was aware of video showing an officer speaking to a member of the public at the Palace of Westminster.

“The public absolutely have a right to protest and we have been making this clear to all officers involved in the extraordinary policing operation currently in place and we will continue to do so,” said Deputy Assistant Commisioner Stuart Cundy.