HSBC says it has now processed 99% of payments which did not go into customer accounts as expected this morning.
The bank apologised again for the inconvenience caused to thousands of people who were due their wages today.
Customers who have not received their money by Saturday morning are advised to contact the bank straight away.
Rebekah Brooks is set to return to Rupert Murdoch-controlled News Corp a year after she was cleared of phone hacking, it has been reported.
The former Sun boss will be appointed chief executive of its UK division as soon as September, according to the Financial Times.
ITV News understands Mrs Brooks is expected to take up the role in the coming weeks.
Brooks was cleared of all charges following a 138-day trial at the Old Bailey which saw former News of the World editor Andy Coulson jailed.
A spokeswoman for News Corp said: "As we have said before, we have been having discussions with Rebekah Brooks and when we have any announcements to make we will let you know."
Thousands of customers have been left without their wages ahead of the Bank Holiday weekend. Here is what we know so far.Read the full story ›
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.
HSBC said around 275,000 payments like to total hundreds of millions of pounds have been held up by a technical glitch.
The fault in the payments, which has affected many people due to receive their salaries for the month, relates to the bank's business customers.
HSBC said it was working to resolve the problem but it still did not know whether it would be able to process the payments by the end of the day.
A spokesman said: "There has been a fault in the information used to process some payments from HSBC business customers.
"Approximately 275,000 payments have been affected, including payments to customers of other banks.
"We will work with other banks to ensure that customers do not lose out as a result of today's problems."
The bank has apologised to customers after issues thought to be with the Bacs system leave many without their salary.Read the full story ›
Britain's service sector enjoyed its best performance in 17 years, with firms in areas such as accountancy, law and marketing bouncing back after a weak start to the year, figures show.
The Confederation of British Industry said business and professional services had reported their best-ever period in the three months to August, according to data going back to 1998.
The services sector represents more than 75 per cent of UK output.
Thousands of schoolgirls will be encouraged to consider a career in engineering as part of a new scheme by Network Rail.
It follows research revealing girls as young as seven have an "unconscious bias" against the profession - with most having switched off to the idea at all by the age of 14.
The firm warned that bias in adults such as careers advisers on what jobs are suitable for girls are partly to blame.
Network Rail chief engineer, Jane Simpson, joined the company as an apprentice aged 16 - and now managed a 500-strong team of engineers and technicians across the country.
If my school careers adviser had her way, I would have become a nursery nurse or teacher but I wasn't willing to accept being pigeon-holed like that.
As part of the drive, schoolgirls will be offered work experience and introduced to the railway industry via open evenings.
Network Rail said ensuring the industry was open to all helped nurture a diverse workplace, which studies have shown helps to "increase productivity and creativity".