How long ago was the card replaced? I worked in debit cards for Natwest for 3 years, and we could see old cards on the systems for the last couple of years. The systems did get purged from time to time though.
I'd recommend getting your mum to contact her bank and see if they can give her the information. She'll probably have the most luck physically going in to a branch, as a lot of people won't give any card information over the phone (although it's unlikely for someone to have all but the last 4 digits anyway). She will have to know how many cards ago it was, but that can be worked out if you know when you signed up.