Lloyds Banking Group has suffered problems from the start of Monday with the Faster Payments System that transfers funds into and out of accounts.
The system is designed to see money transferred within a few hours into people's accounts.
The problem had a knock-on effect for customers of other banks.
However the bank said that as of 17:00 on Monday the problem had been resolved.
"We are aware of an issue that affected some faster payments earlier today, and apologise to customers that were affected," said a bank spokeswoman.
"All other payment services were unaffected, ensuring that customers could continue to process the significant majority of transactions."
A spokeswoman for the Payments Council, which oversees UK payments strategy, said the problem had been with Lloyds Banking Group, which had not been able to send or receive customers' faster payments.
"This is the system that is used to process telephone, internet and standing order payments," she said.
"This is not an issue for the central Faster Payments System, or any systems processing other types of payments, which continue to operate as normal."
Lloyds said that all of its other payment services had been unaffected by the problem, and that customers could still process the "significant majority" of their transactions.
Under the scheme, launched in May 2008, money moved between two participating banks should clear within 24 hours.
The Faster Payments System was set up because bank customers found it frustrating that transferring cash from one account to another at a different bank took several days.
The problem seems to have originated at the weekend.
Some bank customers had reported waiting for money, including wages, to be transferred into their accounts, and now not knowing when the payments would arrive.