.net.uk and .ltd.uk are also regulated to some degree. You have to be an ISP (or very similar) for the former and have to provide proof you’re a real limited company (by way of company number) for the latter. There may be others.

In fact, I think a company number might have been required to get a .co.uk at one point.

Caveat: This knowledge is mostly from before they opened up the second level for registrations. Originally there was a fixed list of second level domains all under control of the same entity, and they lasted a surprisingly long amount of time before going for the money grab of opening it all up.

I daresay that there are still restrictions on that. I can’t imagine they would have let police.uk go to someone other than, you know, the police.