Silicon.com was contacted by one customer of the Clydesdale Bank, who was told that her MasterCard details, along with those of 2,000 other people, were "in the hands of a fraudster."
The theft was detected and the card stopped before it could be used by the fraudster.
The Clydesdale Bank would not comment except to say it was advised of the problem by MasterCard.
MasterCard said it took immediate action together with all the banks concerned.
"In order to protect cardholders, MasterCard and its card-issuing banks operate state-of-the-art, multilevel fraud-monitoring systems," MasterCard said in a statement. "Together, we look for patterns of activity consistent with fraud. Issuers can then monitor their cardholders' accounts closely for fraudulent activity and may reissue cards or take other actions if they suspect fraud has occurred."
MasterCard, whether it was limited to the U.K. or which issuing banks were affected besides the Clydesdale.
Andy McCue of Silicon.com reported from London.