The arrests of protesters after the death of Queen Elizabeth II are "deeply concerning", free-speech campaigners have said.
Police in Scotland have charged two people, while a man was arrested and de-arrested in Oxford.
The arrests came at events to mark the Queen's death and proclaim King Charles III Britain's new monarch.
In London, as queues began for the lying in state, the Met Police said people "have a right to protest".
A 22-year-old man has now been charged in connection with a breach of the peace after the Duke of York was heckled during the procession of the Queen's coffin in Edinburgh on Monday.
Videos on social media showed a man shouting at Prince Andrew as he walked behind the hearse, before being dragged to the ground by two bystanders.
It comes after a 22-year-old woman was charged in connection with a breach of the peace after an accession proclamation for the King outside St Giles' Cathedral a day earlier.
Both have been released and will appear at Edinburgh Sheriff Court at a later date.
On the same day, Symon Hill, 45, was arrested on suspicion of a public order offence after shouting "Who elected him?" during another accession proclamation in Oxford.
Thames Valley Police said he was later de-arrested and was assisting officers "voluntarily".
Also on Monday, a protester holding a sign reading "Not my King" outside parliament ahead of the King's arrival at Westminster Hall was ushered away by police.
The Metropolitan Police said, external a member of the public had been asked to move from outside the Palace of Westminster "in order to facilitate vehicle access and egress through the gates" but had not been arrested or asked to leave the wider area.
The Met also responded to a video circulating on social media in which an officer is heard asking for the details of a man who had held up a blank piece of paper and expressed an intention to write "Not my King" on it. The officer - who was reportedly from another force brought in to assist the Met - is heard saying the message "may offend people".
A statement, external from Deputy Assistant Commissioner Stuart Cundy reads: "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."
Around 1,500 military personnel will work alongside police and civilian stewards to manage the huge numbers of people expected to flock to London over the next week.
The new Metropolitan Police Commissioner Sir Mark Rowley has said his force faced a "massive challenge".
"We will have a safe event, but we're going to be putting thousands of officers into this because of the level of security required and the millions of people who want to pay their respects," he said.
The prime minister's spokesman would not comment on individual arrests, but said: "More broadly, obviously, this is a period of national mourning for the majority, the vast majority of the country.
"But the fundamental right to protest remains as a keystone of our democracy."