Further comments having actually read the page:
Membership should be open to non-residents, especially if they have some connection to the UK (non-resident UK citizen, for example). The use of proxies means having non-resident members doesn't make it harder to find a quorum. I also see no reason to restrict it to over 16s. Under 16s can't be on the board, but they can be members as far as I'm aware (I've read the appropriate Act and didn't see anything in there about age restrictions on members). I also don't know of a requirement for a parent's signature, but it probably wouldn't hurt - the £1 liability probably wouldn't be binding without one, but that's just a nominal amount anyway.
It should probably be made clear that the register of members will be made available to anyone with a good reason for asking (that's a legal requirement, I don't remember the definition of "good reason").
"Guarantor" isn't a class of membership, it's just an adjective we use to make it clear we're talking about legal membership of the company rather than being a "supporting member" as v1.0 called it (I think it's been agreed that we should rename that "friend" if we have a similar concept to avoid confusion).
I believe holding membership details for 10 years is, indeed, a legal requirement. I don't know of any requirement to keep hold of the actual application form, though.
I'm not sure it's a good idea to explicitly restrict the reasons the board can refuse membership. We already have an appeals process, so just let the board use their discretion about what is in the best interests of the charity. It may also be good to add "not disrupt the charity" to "not bring the charity into disrepute".