In order to change the listed owner/registrant for a .co.uk/.org.uk/.me.uk domain name you will need to login to your Nominet (the Internet registry for the .uk domain name extension) account at https://secure.nominet.org.uk/auth/login.html
Once you are logged in you will need to click on the 'Registrant Transfer' link. This will take you through the process of transferring then domain to another party. There is a charge for this of £10.00 + VAT
When the details are complete the new registrant will be contacted and have 5 days to accept the transfer. If this does not happen Nominet will refund the charge and the process will have to be started again.
You can find more information on the process at http://www.nominet.org.uk/uk-domain-names/manage-your-domain/transfer