VMC-on-top: It's also recommended that you do a mortgage search on an aircraft before you commit to purchasing it (CAA Form CA350
Form CA350: Search of the UK Register of Aircraft Mortages | Publications | CAA). It costs £25 but could save you considerably more if you accidentally purchase an aircraft with a mortgage that hasn't been completed by the previous owner!
Lister: Unusual Attitude is spot on regarding the CA1 form - provided this is complete correctly along with payment, and the previous owner's Certificate of Registration (CA71) has been signed on the back then it should be fairly smooth. Not forgetting proof of insurance at the same time, unless you've declared that the aircraft won't be flown.
Another thing to consider if there's a group of you is whether you all want to appear on the registration document, or whether you're going to nominate you or someone else within the group as the group trustee. The advtange of nominating a trustee is that all future correspondence goes straight to them, and your only obligation if someone enters/leaves the group is that you notify the CAA using the trustee grid
http://www.caa.co.uk/docs/122/trusteegridblank.pdf. You'll also need to complete this grid when you send in your initial application. If you
don't want to nominate a trustee and would all like to appear on the Certificate of Registration, then you need to bear in mind that you'll have to apply for (and pay for) a change of ownership whenever someone joins/leaves the group.