The WHOIS UK Lookup tool provided by Nominet provides full details for all .UK domain names. This can include owner details and addresses where permission has been granted.
Nominet is the official register governing all .UK domains. This includes all .uk as well as .cymru and .wales.
In the past all details on Whois UK were available to the general public. This has since changed to a permission based system where owner details are hidden unless consent has been granted. You can still obtain the non public information about a domain owner through a data release request. This is a form you must fill out providing reasons at to why you are wanting the information. A few examples of legitimate requests are displayed on site.