Bank bosses should be subject to a "detailed investigation" over the IT meltdown which left thousands of customers without access to cash, Bank of England governor Sir Mervyn King has said.
His comments came as Ulster Bank owner Royal Bank of Scotland said it hopes to restore a full service for customers in Northern Ireland by the start of next week.
It had more success across the Irish Sea where it has successfully updated all but 1% of NatWest and RBS account balances.
Sir Mervyn told MPs there would need to be a "detailed investigation" into what went wrong and why it has taken so long to sort the issues out.
RBS and NatWest have around 15 million accounts between them, but it is still unclear how many were affected by the disruption.
A spokesman for RBS Group said it may "never know" the exact figure as it was not possible to tell when everyone is expecting money to be paid into their account and some people may not have noticed problems.
Ulster Bank has estimated that about 100,000 of its customers have been caught up in the problems, which have meant that customers' balances have not been updating properly and their wages have not shown up in their accounts, although the money is "in the system".
The Financial Ombudsman Service (FOS) warned that it could be weeks before customers see all of the issues completely resolved.
In a statement issued yesterday, RBS Group said a "small number" of customers may continue to be hit by the "unacceptable" delays.
The statement said: "We know this disruption was unacceptable and that many customers will still have questions and concerns.
"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.
"We are confident that this will help us restore a full service for the start of next week for Ulster Bank and remain grateful for our customers' patience."
The banking group has extended its opening hours this week as staff work "round the clock" to sort out the problems, which began after a software update last Tuesday.
People have had their house moves and holidays disrupted and a defendant in a court case had to spend the weekend in prison because the RBS computer failure prevented his bail money being transferred.
In a hearing with the Treasury Select Committee, Sir Mervyn said the Bank had been in close contact with management at RBS since the problem arose, and over the weekend. He said the issues were technical and not a reflection of funding issues at the bank, which is 80% state-owned.
He added: "Once the current difficulties are over, we need the Financial Services Authority to carry out a detailed investigation to find out what went wrong - and importantly why it took so long to recover."
Sir Mervyn said the problems seen at RBS provide a reminder of how systemically important banks are and confirmed the need to ring-fence retail operations from investment banking.