Hey Hagar, i bought my car while the seller was in the process of the private reg transfer.
The way he did it was to take the application to the local DVLA office and got the V5 section 10 back stamped with the new (old / reverted / whatever you want to call it) plate and the form allowing tax to be bought on the new plate, and a tax disc on the new plate to replace the one tied to the private plate.
At that point I bought it without the full V5 on the new plate. The risk to doing so is mainly to the seller in terms of fines etc, as the DVLA still see it as your car even though ownership has passed to the buyer, as the receipt proves it has.
The buyer got the full new plate V5 back 2 weeks later, we filled in our bits, sent it off and now have the proper paperwork back for all.
The problem is that the biuyer wont be able to status check with the RAC etc until the plates change.
It was a bit of a pain, but not huge.
Apologies for the crap explanation - off out and in a rush. If that makes no sense and you want a better explanation, feel free to PM