.uk domain names can be registered by anyone located anywhere. However, if the registrant is located outside of the UK, the admin contact must have an address in the UK to serve as an "Address for Service".
Address for Service
When the registrant (owner) of the domain is outside of the UK, the admin contact must list an address located in United Kingdom (GB), Guernsey (GG), Jersey (JE), or Isle of Man (IM).
PO Box Addresses
These are not permitted on second level .uk registrations for the registrant or admin contacts (more info).
.CO.UK / .ORG.UK Domains
.co.uk and .org.uk domains can be registered by anyone located anywhere. These names can be registered with an address from any country for both the registrant and admin contacts.