Many people are unable to withdraw cash, or use their debit cards to make purchases.
Lloyds say they are working to resolve the problem.
A Lloyds Banking Group spokeswoman said: "We are aware that some customers are unable to use their debit cards either to make purchases or to withdraw money from ATMs.
"We are working hard to resolve this as swiftly as possible and apologise for any inconvenience caused."
Disgruntled customers expressed their dissatisfaction on social media.
Carl Bullivant tweeted: "Wife's card declined in Asda had to go get my card from home how embarrassing standing and waiting #poorbankingservice."
Essie Young wrote: "Didn't even want to be a @TSB customer when LTSB split! Couldn't buy my twins bday presents today with TSB card! #fuming #customerservice."
Another customer tweeted: "@TSB left me unable to pay for my shopping and no access to my money. TSB are a joke."
Another Twitter user wrote: "This problem is also affecting Halifax debit cards as I found out trying to pay for lunch with my wife!"