I think this game is called "Let's validate the bully," because rarely do schoolyard fights start, in my experience, other than where one of the protagonists is more or less completely certain that they can beat the shit out of the other:
Union warns teachers not to break up playground fights
The local council, in this case, refused to compensate the injured teacher, because it had not been negligent. However, if a child suffers injury, because staff refuse to intervene, then the council most fucking certainly will be negligent, and should duly be strung up by the balls before the civil courts, for deliberately doing nothing to intervene.
Much more to the point: this just smacks of cowardice, and schools should not be surprised to find that parents are unwilling to send their children into an environment, which is potentially dangerous. You want authority, motherfuckers? Then accept the responsibility that goes with it.