The police don’t charge at will mate an order has to be given based on the threat level and the actions of the crowd.
The person giving the order will be sat miles away monitoring a live feed, with an acute awareness that the whole thing will be on social media in seconds and all that that brings. The whole situation will have been evaluated based on restoring order and regaining control of the situation as quickly as possible, before it gets totally out of hand.
It’s not just one of the coppers shouting “ charge “ and all the rest piling in.
The police in this country have always used horses for crowd control. It's been used in sporting events including football matches since before I was born and you rarely hear of any problems, except when having to deal with the odd bout of football violence. But yeah, maybe we are stuck in 1902. Perhaps we should be upgrading our police force so they have armoured cars, water cannons, CS gas and rubber bullets. That's what most of the rest of the world does.
Also, what country, anywhere in the world, wouldn't have a protective layer surrounding the residence of it's most senior politician, especially when significant protest marches are taking place locally. In fact, anywhere else that protection would consist of a damn sight more than a few police on horses. And imagine expecting said protection unit to idly look on whilst flares and missiles are thrown at the senior politicians home. Of course they would be expected to maintain control of the area.
And what was defacing the Cenotaph all about?
Having said that, I have no doubt that the vast majority of the protestors had only peaceful intentions, and that many of them did their level best to socially distance. The people that did this were just scum that go around attaching themselves to peaceful protests.