Dont pay for whois privacy for UK names. All you need is to go to Nominet and on there you will have to fill in a form basically saying you are a UK resident, your status is that of an individual and you`d like to make your info private.
Things are changing in .uk as of 1st March 2016. Nominet Registrars can now offer a privacy service in partnership with the registry. Some Nominet registrars had been offering full WHOIS privacy on .uk domain names but the new system has benefits for both registrars and the registry as detailed. With this service both the Registrant Name and Registrant Address will be hidden from both the WHOIS and from the Nominet Searchable WHOIS (formally known as PRSS).