HSBC has said all of the 275,000 payments held up by a glitch today would be processed by tomorrow morning.
The failure left many workers without their monthly salaries going into the Bank Holiday weekend.
HSBC said it would now process most of the payments this afternoon and evening with the remainder completed overnight.
The bank said: "HSBC apologises for the significant inconvenience caused to customers by today's payments problems.
"We are now processing the payments so that they reach the beneficiary accounts as quickly as possible. The majority of payments will be completed over the course of the afternoon and early evening, with any remaining payments completed overnight.
"We are committed to ensuring that no one loses out as a result of today's unacceptable problems. We will work with our customers and the other banks including providing compensation where appropriate.
"Customers who do not receive the delayed payment by Saturday morning should speak with their bank in the first instance. They should also contact their bank if they have suffered any costs as a result of today's problems."