Scotland’s chief constable has been told of free speech concerns amid the arrest of anti-monarchy protesters in Edinburgh.

Conservative MP David Davis has written to Sir Iain Livingstone after a 22-year-old woman was arrested in connection with a breach of the peace during the Accession Proclamation for the King outside the city’s St Giles’ Cathedral on Sunday.

Following his letter, another alleged protester, a 22-year-old man, was arrested on the Royal Mile as footage appeared to show him heckling the royal procession.

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In his letter, written on Monday, the MP for Haltemprice and Howden said: “It is not for me to interfere in the judicial process. However, with the accession of our new monarch, I would hope that the police will continue to respect the right to free speech.

“If the individuals concerned committed acts of violence, or the police had reason to believe she would, then action was obviously necessary.

“But if the individual was simply stating an opinion, I trust you agree that a liberal approach would be desirable.”

After learning of a second arrest in Scotland, he wrote on Twitter on Tuesday: “At a time of national mourning, we should all ensure that we behave respectfully.

“But we must not sacrifice the principle of free speech upon which modern Britain is built.

“I am a staunch monarchist, but republicans have as much right to voice their opinions as anyone else.”

Scottish MP Joanna Cherry has also raised concern over the arrests.

The SNP Edinburgh MP said: “I’m concerned by reports in Scotland & England of seemingly legitimate protesters being arrested.

“Whilst many might question whether this is an appropriate time for such protests, the right to protest is fundamental to our democracy & should be facilitated.”

In Oxford, a man was arrested on suspicion of a public order offence after shouting “who elected him?” when he came across a public formal reading of the proclamation of accession for the King. He was later de-arrested.

Meanwhile, a protester bearing a handmade sign saying “not my King” was spoken to by police and escorted away from the Palace of Westminster.

A Police Scotland spokesperson said: “We’ve received correspondence and the content is noted.”