There is no permission requirement. I could setup blah.uk without notifying you.
What you can't do is to pass yourself off as another entity. So if I registered apple.uk and sold fruit and veg I would probably be ok, but if I used the same name to sell computers or phones, I might get a call from a certain company's legal team if they became aware of it (usually happens when the business grows). There are some rules around companies having the rights to their own name, and there have been a few court cases where disputes of this nature have been resolved.
If you've received a request for a company looking to setup blah.cn, it might just be the company is looking to avoid any conflict in the future ... if they have confirmation from you that they can proceed using that name, then you would not be in a position to challenge their right to the name later on if, for instance, you wanted to start trading in China.
It all does sound a bit unusual though.