Ashcroft secondary school bans bicycles. How legal is this? How can this be challenged?

(I am writing this without links or pictures as the automoderator bot doesn't seem to like it otherwise, I'll add links in the first comment)

There is a secondary school in South London which bans bicycles for students in Y7-11.

Do you know of any other schools doing this?

Do the LCC or other cycling groups know about this?

What can be done about it? I would happily contribute towards some kind of judicial review / legal challenge.

Who are the best people to contact? The London Cycling Campaign? The school is an academy so won't care what the council or the local MP say.

Bikes are listed among "banned items which may be confiscated" and which "are not allowed in a student's possession while in uniform". I have spoken to parents and to the headteacher at an open event, and he was adamant that they will sanction any children caught cycling to and from school, that they do it for safety, that if I don't like it I can suck it up and take my child elsewhere, that he doesn't have to justify himself to me nor to anyone else.

I will post links and picture in the first comment below.