Ash83,
Not clear why your mother has appeared to have left this for a year before querying, probably doesn't help the situation, however....... from experience, the actual cause is one of the following..........
a) the person took out the money themselves, but doesn't recall doing so immediately (doesn't appear to be the case in here, as the money was taken out of a machine your mother never attended
b) card was skimmed, elsewhere and used here (possibility)
c) PIN was with card (yes it happens frequently, despite the warnings re same) and was used by either a fraudster or would you believe often a family member - don't panic I'm not accusing anyone in your family. I'll assume the PIN wasn't with the card, therefore we are really left with option b).
Did you get to ascertain if there was a security camera on the ATM that was used for the withdrawal? If so, they should be able to tie down who used your mothers card (or at worst, at least prove it wasn't her). The time delay might be an issue here at this stage.
My own approach when this issue arises, is to see how long the customer has been banking with us (I work on the basis if the customer has been banking with us a long time they are unlikley to 'do' us for the sake of E2/300, and in the long run the goodwill generated pays for itself), to meet with them to discuss, and more often than not you will realise the customer is genuine, and I'll take the loss and make the refund. Also important to cancel the existing card (in case it has been skimmed, and re-issue a new (not replacement one)).
Perhaps you've done/discussed all of the above with your bank, if you have and are still not happy, you should either contact their Customer Care Centre or the Ombudsman to see if same can be resolved. If you haven't done/discussed the above, I think it would be worth a try.
Best of luck...........
BM