It depends on the bank but some banks offer some kind of statement search facility on internet banking. Alternatively if you knew the year of purchase you could ask the bank to produce a paper copy of that years statements. I guess they may be able to charge you for this but again it would be dependent on the bank itself.
If several hundred pounds were at stake, or for simple principle, I would certainly give them a call and ask for assistance.
EDIT: Cash deal is obviously not provable without the original receipt.
