They can also require web filtering and surveillance software, of course.
In many schools, this kind of software, web filtering (including filtering of proxies and category of SSL-based websites) is ACTUALLY REQUIRED in the US, for many schools to keep funding under various federal programs -- eg E-rate.
I'm not going to pretend I know the US law. Or even UK law, for that matter. IANAL
Sure, there are things that may be tweaked by the school, but the are laws setting the basic boundaries for such modifications.
Well, they are perfectly within their rights to provide a policy of "No laptops allowed past this point", at the door.
I'm fine with "no laptops allowed past this point" policy. Heck, I'm fine even with monitoring the traffic, assuming it's publicly announced. What I'm not OK with is when this happens in secret, without telling anyone.
Anything less is a concession on their part.
In the case of your physical PERSON, they can't require arbitrary concessions, such as body cavity searches without infringing on people's rights.
With laptops however; they can require arbitrary modifications or standards of their choosing, before the laptop is permitted access.
Fully updated, not running an EOL operating system such as Widnows XP, No infections present and working antimalware, would be some common restrictions.
There may be differences between US/UK, and the part of Europe where I live. Here we have "privacy of correspondence" which applies even when I (for example) access my personal email while at work. Or whatever. So no, it's not just about physical person - at least not universally.