HSBC said payments which did not go in people's bank accounts today should be there by tonight.
A statement released by 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.
"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."
They added they would ensure no one loses out as a result of "today’s unacceptable problems" and said compensation would be offered where appropriate.
The family of dad-of-one Tony Brightwell, the seventh person identified to have died in the Shoreham air crash, described him as a "kind, loving man".
The 53-year-old Health Care Manager for Sussex Partnership NHS and Brighton and Hove City Council was engaged to Lara who described him as her "soul mate" and the "love of her life".
Mr Brightwell had a passion for planes, cooking and cycling and his family said he was "very excited" about seeing one of the last flights of the Vulcan bomber.
He had gained his private pilot licence many years ago at Shoreham and regularly went to the airfield to watch the planes take off and land there, the family statement said, with a view that he "might take up flying again one day".
"He had a real admiration of Second World War pilots and the huge, terrifying responsibilities that men and women faced," the statement said.
The family thanked everyone that had sent "love, condolences and prayers", adding: "While we appreciate that many others will be experiencing similar unspeakable grief in such tragic and public circumstances, (we ask) that we now be allowed to grieve ourselves in private and in peace."