I'll suggest that this sort of thing is worthless in any sort of legal contractual context. The fact that it comes from a school doesn't make the writer any sort of lawyer. (Last winter my grandchildren's school had signs up saying that some access paths within the school grounds were icy and people used them at their own risk. Nonsense. I fancy that the only legal significance is that it shows knowledge of the danger. ie it's an unfair disclaimer.)
The legal niceties don't matter because for most people, and as has already been suggested, enforcement comes through a form of blackmail: many (most?) parents don't want to be in conflict with a school, nor do they want to prepare bullets for their children to fire.
Presumably, backside covering is at the er, bottom of this. I can understand that a head teacher would not want to be in a position where a child was injured on the way home from school and a parent complained that they didn't know that the child was being allowed to leave school in some way unprepared for the journey. The way round that must surely be written parental consent required for any pupil cycling to and from school under each parent's own rules. (Before anybody says the obvious, it's something the LEA's legal department would have to word.) Beyond that, I wonder if there's a concern that any parent allowing their child to cycle without a helmet is ipso facto
guilty of a form of child neglect which a school could not tolerate.
Without involving anybody in the underlying helmet debate, there must be a head teacher or two who is/are forum member(s.) Perhaps somebody could explain what it is that these staff room lawyers are concerned about?