The co.uk domain is for the registration of names relating to commercial enterprises.
No limitation is placed on the number of names that may be applied for or the use for which they are being put to subject to any request meeting the rules as applying at the time when the request is made.
SYNTAX rules for domain name requests. [These rules apply at the top level of delegation only: e.g. the "xxx" in xxx.co.uk, xxx.tv.co.uk, and so on, but not within a delegated domain.]