It is, and some people got arrested for protesting. I think two people in England were arrested then de-arrested for having signs along the lines of “not my king” or “not elected”, while someone in Edinburgh has been arrested and charged for shouting at Prince Andrew while he was following the coffin procession, though the BBC neglected to say what was shouted.
To be fair, it's a bit more complex than just arrested for protesting.
Behaviour likely to cause a breach of the peace was brought into UK law to deal with the scenario in which British Nazis (the blackshirts) were going around and provoking people into fights, and then claiming self-defence. So Breach of Peace laws enable people who do behaviour that is clearly trying to provoke others around them into violence to be arrested and held liable for that clear provocative behaviour. But it doesn't cover clear protest.
Now, we find ourselves in a grey area this then creates: If you go up to a gathering of mourning monarchists that is also a precession of a new monarch, and shout "abolish the monarchy"...are you legitimately protesting against the precession of the new monarch, or are you engaging in behaviour that you could reasonably expect to be provoking the mourning monarchists to violence?
And then, if police feared the latter but wanted to give benefit of the doubt for the former, then you could argue escorting them away but then de-arresting them is the best option available to them.