I was going by the two registrars I know of that do privacy on .co.uk - neither have the option to add it to a .uk (godaddy and 123-reg).
I take it you know one that does?
I see. Not completely off hand but I could suggest some that probably do. LexSynergy might do. KeySystems might do. Netistrar probably do.
Just to differentiate between the various privacy and opt-out services available:
1.
This is WHOIS opt-out for individuals who wish to opt their address out of being displayed in the WHOIS and the
rules on who can opt out.
2.
This is Nominet's own registrar privacy framework, that registrars can sign up (for free) to use and offer a registry powered privacy service which hides both address and registrant name in the WHOIS although the registry does get a copy of this data.
Please see page 12 within
this document for WHOIS output examples of (1) and (2).
3. Some registrars offer their own registrar privacy service that isn't registry powered and only the registrar sees the true registrant.
Please see page 4 within
this (the same) document for an explanation of the registries view of the pros and cons of (2) and (3).
Putting said the above, there is no technical reason why any of the above cannot be offered on a second level ".uk" domain name, like it can on a third level domain name. The Address for Service requirement for a foreign registrant with respect to a second level ".uk" shouldn't affect it either.
What I am not aware of is which registrars offer exactly which of the above services I have numbered for ease of differentiation.