RBS says most bank accounts now updated
Banking group RBS has said that 99% of RBS and NatWest accounts have now been brought up to date.
A computer software upgrade at RBS failed last week, disrupting many payments into and out of accounts.
However, RBS added that its Ulster Bank customers continued to suffer "unacceptable delays".
Bank of England Governor Sir Mervyn King has called for a detailed investigation into what went wrong and the time it took to recover.
He added that the problems demonstrated the importance of management focusing on the service function of banking, which was very different from investment banking.
The Financial Ombudsman Service has warned it could take several weeks for bank customers to have all the effects of the account problems sorted out.
RBS said on Tuesday that it had cancelled its planned corporate hospitality at the Wimbledon tennis tournament as a result of the computer problem, saying it would be "inappropriate" to take guests to the tournament "under the circumstances".
The bank said most of the backlog of transactions had been cleared overnight leaving less than 1% unresolved.
It said only "a few specific sets of transactions" were outstanding.
"It is possible a small number of customers may experience delays as we return to a completely normal service," the bank said.
"The full focus of our efforts will now be on delivering the same result for our Ulster Bank customers who continue to experience unacceptable delays to their accounts being updated."
To cope with the extra workload, RBS is opening 1,200 of its main branches earlier than usual this week and shutting them later.
Despite the progress of the bank in clearing the backlog, more bank customers have complained to the BBC about the disruption they have suffered.
Michele from Broadstairs, said: "I bank with Barclays but because my employers use RBS my invoice was not paid into my account on Friday."
"It is now Tuesday and I'm still waiting for my money to be transferred, my rent has not been paid and other bills.
"We went into Barclays to see if they could help us but they said as it was not their error they couldn't," she said.
Alan from Carlisle said: "I can't be the only pensioner whose weekly DSS BACS payment to a building society account has failed to arrive."
Helen from Bedford said: "We were assured our payments would be done by Monday, then today (Tuesday) yet today I receive a text saying it won't be today but no further information on when it will be.
"Plus a payment that should have gone in today hasn't appeared," she added.
Despite the problems, some readers have praised the help given by RBS and NatWest staff.
Noel from Hungerford said: "I would like to send my appreciation of all those members of NatWest frontline staff who have been working long hours under pressure through no fault of their own - they deserve our thanks."
Renu from Reading said: "Accounts are looking up to date. Staff have been excellent."
Earlier, David Cresswell of the Financial Ombudsman Service said the knock-on effects would take longer to identify and rectify.
"It is really important to start making a note of what is happening to you, of conversations you have with people, of difficulties you are facing, or knock-on effects, because this is a ripple effect from the original problems," he said.
"What you need to do is make a clear list of how you have been affected, so you can go back to your bank and say: 'This is the complete picture, how can you help?'"
The sort of problems RBS is expecting to deal with are extra charges for inadvertently going overdrawn or paying a credit card bill late, and making sure that a customer's credit rating is not damaged.
James Jones of credit rating agency Experian said dealing with the problems, especially for customers of other banks, would be a challenge, as they would not be able to tell if a missed payment was due to RBS's computer problems.
"We get data in from so many organisations, every minute of every day, that we don't normally review the data," he said.
Neil Munroe, executive director of the Equifax credit rating agency, said: "We are reliant very much on the data being supplied by the organisations themselves; maybe as a result of this exercise we will get a lot more disputes coming through about those missed payments."
Choice for customers
RBS is planning to liaise with other banks so that their customers who were affected, for instance by not receiving a payment from a NatWest account, are also not left out of pocket.
The bank has declined so far to estimate how many customers have been affected, how many have complained, or how many have used its telephone helpline.
But an RBS spokeswoman stressed that they wanted affected customers to come forward so problems could be resolved.
"We are offering our customers a choice: face-to-face at any branch, over the phone or via postform on our website," she said.
The bank will reimburse customers for the cost of calling its 0845 helpline number.