This answer explains what the WHOIS optout option is, who can opt out.
The WHOIS database shows the names and addresses of .uk domain registrants. It doesn't show other personal information (e.g. no email addresses or phone numbers). However, as the WHOIS database is available for everyone to view, some people may wish to opt out of having their address shown.
The .uk WHOIS privacy option allows private individuals to opt-out of the WHOIS listings.
To opt-out of the .uk database follow the instructions in this article.