According to the availability of the Domain name you can register the domain names with btNIC, but to ensure the patent rights, and other trademarks, btNIC will not entertain domain names, in conflict with this names, or organizations, for which the individual, or groups, must produce a letter from the concerned organization or companies, to register such domain names.

The domain has to match the company name and that company can register as many domain as the company wants with the extension .bt, .com.bt, .org.bt etc.

It is alright to provide us the address in UK or any other country as long as the address provided is a genuine one.