Consumer organisation Which? said some people had reported not being able to make payments online or buy food at the supermarket on Saturday.
Customers in Leeds have taken to social media to express their frustration, with one customer reporting that she was unable to make deposits or withdraw cash.
The bank has advised customers they can access cash from other banks’ ATMs.
It tweeted: “We’re sorry that a technical problem is affecting our services, our teams are working hard to fix it.
“You can access cash from other banks’ ATMs. Please check back here for further updates.”
Gareth Shaw, head of money at Which?, said: “These technical issues will be causing stress for many Santander customers – with people reporting that they have been unable to make online payments or in some cases purchase food in their local supermarket.
“Customers can incur fines, penalties and fees when they’re not able to access their finances, so the bank must offer compensation to all those who have been impacted in this way.
“These problems demonstrate why it is vital that banks invest to ensure their systems are up to the task of protecting their customers’ accounts and maintaining the services they rely on.”