If the domain is owned by a domainer who has their own Nominet TAG, then their tag is mentioned on the whois details which you should then be able to do some basic searches and locate them via that TAG. If they are registered via some of the major registrars like Godaddy, namecheap, 123-reg etc then it becomes a little harder, sometimes its worth trying your luck on UK TLD specific boards to see if people have dealt with that person previously and has their contact details.
Domain tools can also be your friend to see if there are more domains owned by the same person which could be linked to a more friendly Whois......like the .com.