Refund for purchase using card A but no longer have card A

[rainagain]

Whenever I take anything faulty back to a shop that I have paid for with card they always say "do you have the card you originally used to purchase X as we must refund back to the same card under fraud prevention".

This has never bothered me until recently when I switched bank accounts and will therefore be getting a new bank card. If I take something back to a shop after today that I paid for with my old card what will happen? I looked at a few stores online and they all say in their terms and conditions things such as:

"If you have paid by credit or debit card, we will refund the balance to the card originally used".

"If you require a refund, please bring with you the credit/debit/gift/insurance card used to place the order."

I tried a google so see if I could find anything from trading standards, etc about this but couldn't find anything.

Does anyone have any ideas about this?