As I understand it, although this is digging up the memory banks from 7 years ago.....
If the thief take a bike belonging to someone else, that bike becomes stolen property (obviously), and the thief is a thief.
If he/she passes that bike to someone else, who knows the bike is stolen, in order to get rid of it, ie sell on
ebay etc.. then that person 'handles stolen goods'.
The innocent buyer who pays a
'reasonable price' for the goods
(if bought too cheaply, it can be argued in court that you knew the goods were stolen as you paid a ridiculously cheap price for them) as in this case, then that bike no longer becomes stolen property, it is now owned by the new owner.
The money generated from the sale, ie in this case £450 becomes the stolen property, although this part is vague to me at the mo. I will look up later when i get home, and try to clarify, but at this stage you should not give up the bike.