Multiple retailers are reporting problems processing debit and credit card payments due to the issue, which is related to Visa payment processing across Europe.
Because Visa run a lot of the payment systems, all credit and debit cards could be affected by the problems.
Reports suggest Tesco and Sainsbury's and multiple other retailers are affected as well as Asda.
Customers at Asda in Leeds say the supermarket is one of those having trouble with cards.
A spokesman for the retailer said: "The issue is intermittent, so it's not all cards, it's not all stores and it's not all checkouts. It's certain cards, certain checkouts, certain stores.
"Where a card payment is declined we’re asking customers for alternative forms of payment, ie cash, or another card.
"Right now, you may expect, just as in any other affected retailer, not to necessarily have the smoothest journey through the checkouts.
"For that we can only apologise and we are working hard until we’re able to resolve it.
Asda is advising customers to bring cash if possible if planning a trip to the store tonight.
The spokesman added: "We will attempt card payments and there are certain things we can try at the checkout to get people through."
Visa across Europe
Visa card payments are failing across the UK and Europe.
The company said it is working towards resolving the problem.
Visa users have taken to social media to complain, and it is understood the Bank of England is aware of the issue and is in touch with Visa.
A Visa spokesman said: "Visa is currently experiencing a service disruption.
"This incident is preventing some Visa transactions in Europe from being processed.
"We are investigating the cause and working as quickly as possible to resolve the situation."
HSBC's UK Twitter account replied to a customer query on Twitter: "We believe there may have recently been issues with Visa's payments processing.
"From what we understand there are still intermittent issues but services are slowly recovering."