A legal expert has said people protesting peacefully against the monarchy "should be left alone" by the police following two arrests as Charles III was proclaimed king.
A man was arrested in Oxford and a woman was arrested in Edinburgh as they protested on Sunday during proclamation events.
But human rights barrister Adam Wagner said people should be allowed to protest peacefully.
He wrote on Twitter: "A few stories of people being arrested for protesting against the monarchy - unless they are threatening violence the police should leave well alone.
"Freedom of speech is as important a value in times of public mourning as it at any other time."
He added: "A few people saying, 'Now is not the time'. That is a fair opinion and will be shared by many, but it is an opinion not the law. Protest is often inconvenient and irritating - but still a central part of our democracy."
Jo Maugham, a barrister and director of the Good Law Project, said the arrest of a protester in Oxford was "powerfully vindicating concerns about the new totalitarian restrictions on the right to protest".
Under the Police, Crime, Sentencing and Courts Act, which was updated earlier this year, police can now impose start and finish times on protests, set noise limits and apply such rules to a demonstration by just one person.
Watch: Protesters boo during ceremony proclaiming King Charles III
In Oxford, author, activist and history tutor Simon Hill said he was arrested and subsequently de-arrested after he called out, "Who elected him?" during Charles's proclamation, as he came out of church.
He told the Bright Green website that officers gave him "confused answers" when he asked why he had been arrested.
He said he had not objected to people mourning the death of Queen Elizabeth II.
"It was only when they declared Charles to be 'King Charles III' that I called out, “Who elected him?”
"I doubt most of the people in the crowd even heard me. Two or three people near me told me to shut up. I didn’t insult them or attack them personally, but responded by saying that a head of state was being imposed on us without our consent."
Thames Valley Police told Yahoo News UK: "A 45-year-old man was arrested in connection with a disturbance that was caused during the county proclamation ceremony of King Charles III in Oxford.
“He has subsequently been de-arrested and is engaging with us voluntarily as we investigate a public order offence.”
The force said the man was arrested on suspicion of a public order offence.
In Edinburgh, a woman was arrested after a protester held an anti-monarchy sign ahead of the accession proclamation of King Charles III.
Police Scotland said the arrest was made outside St Giles’ Cathedral, where the Queen’s coffin will rest on Monday.
Moments before the proclamation on Sunday afternoon, a demonstrator appeared in the crowd opposite the Mercat Cross.
She held a sign which read: “**** imperialism, abolish monarchy”.
Officers appeared behind her and took her away, prompting the crowd to applaud.
One man shouted: “Let her go, it’s free speech,” while others yelled: “Have some respect.”
A Police Scotland spokesperson said: "A 22-year-old woman was arrested outside St Giles' Cathedral, Edinburgh on Sunday, 11 September 2022 in connection with a breach of the peace."
It came after hecklers were heard booing during the event.
During the first proclamation of Charles, the Lord Lyon King of Arms gave a speech before declaring “God save the King”, which the crowd repeated.
One man was heard booing throughout the cheers.
The national anthem was then sung but, afterwards, people could be heard calling for a republic.
Watch: Proclamations for the King take place across the UK