Lister,
Print out & complete form CA1 which you can get from here:-
Form CA1: Registration of Aircraft or Change of Ownership | Publications | CAA
Send it off along with the correct fee and the existing registration documnent which should have been signed over to yourself by the previous owner, (section on back of document), previous owner may have sent this off to the CAA for you already.
Changeover should only take a few days and you can keep an eye on it on GINFO.
Hope this helps!
Regards
UA