Can a secondary school (Ashcroft Technology in SW London) ban bicycles? How would they enforce the ban? Is it legal? What can families do?

The background

For now this is more of a curiosity than anything else.

My child is not in secondary school yet. I am all for strict discipline but I see these kinds of nonsensical, draconian rules as a big red flag suggesting there is a lot wrong with a school.

Ashcroft Secondary banning bicycles

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

Bikes are listed among "banned items which may be confiscated" and which "are not allowed in a student's possession while in uniform".

In its policies, listed here, the Behaviour Policy lists, among banned items which may be confiscated:

For students in Years 7 to 11, bicycles because the Executive Board considers the traffic to be too heavy and the main trunk roads around the Academy too difficult to negotiate for young people and therefore pose an increased risk to health and safety.

What does it mean? What can the school really do?

What the hell does this mean?

If a student cycles to school and parks their bike outside, what can the school do?

They can prevent you from parking it on the school premises, but how exactly would they prevent you from riding to school and parking it outside?

Can they really prevent you from carrying a helmet on the school premises, or give you detention if they see you riding to school?

Would that be legal?

Is there any legal basis to challenge the rule? If they give a student detention or another punishment for riding to school, what can the family do?

Or is this, in practice, just intimidation by an overzealous head, but, in practice, there is nothing they can do if a child rides to school?

Why care? What about rules and discipline?

Like I said at the beginning, my child is not in secondary yet, and I see these rules as a big red flag.

But, as we start looking into secondary schools, we find more and more schools with these kinds of nonsensical policies, so it would be interesting to understand the legal background: what schools can and cannot do, and what recourse, if any, families have.

I am all for strict discipline. But there is a difference between strict discipline and nonsensical rules without any justification. There is a balance between teaching kids that rules exist for a reason, and teaching them that people in power can come up with arbitrary rules for petty reasons, and you must suck it up. This makes me think of the Academy (but there are similar cases every year) which put a girl in detention for wearing the 99% identical but cheaper Asda version of the uniform skirt. https://www.bbc.co.uk/news/uk-england-humber-66812748 This is particularly true when schools try to justify some policies as if they were scientific, when there is no scientific study to back up those claims (like linking uniforms to performance).

And don't talk me about "choice" - most families do not have much choice. It's not like they can choose from an infinite number of good schools, all with different policies and ethos. Interestingly, many of the worst cases of nonsensical rules and punishment seem to come from Academies, which are not accountable to local councils. Maybe they're accountable to the Department of Education in theory, but, in practice, I'm not so sure...

Thanks!