//...someone being inconvenienced or... "spoilt enjoyment"... is not a matter for the metropolitan police.. so the thing you describe is not a trouble at all//
If it has potential to cause a breach of the peace it is a police matter. Whilst is is not an offence, action likely to cause a breach of the peace gives a police officer the right to warn the culprit of his behaviour and if he continues, to arrest him. These nerds are very likely to incur the wrath of those wishing to enjoy the occasion (as the "Just Stop Oil" people are beginning to discover). It has the potential to get ugly, so it is a police matter. If that (i.e. preventing potential disorder from breaking out) makes the UK a police state then I'm all for it.
Quite honestly, I don't know where they left their sense. The crowd who have bothered to stand out in the rain to watch the Coronation procession are highly likely, in the main, to be staunch Royalists, as are those watching at home on the TV. The sight of someone waving a piece of cardboard emblazoned with the words "Not My King" or some similar pathetic drivel (because he is their King, whether they like it or not) is hardly likely to suddenly convert them into ardent Republicans.
BTW, my reference to making the place look untidy was flippant. But my idea to restrict protests to places where they won't cause any upset or inconvenience is not (though I will look at Hopkirk's request to reconsider the venues).