NatWest branches were being kept open late today to help a "large number" of customers who have been affected by technical hitches which failed to properly update their account balances.
The problems, which meant people struggled to use online services, have also affected Ulster Bank customers and a "small number" of customers who use the Royal Bank of Scotland (RBS), which belong to the same banking group.
More than 1,000 NatWest branches in major towns and cities were being kept open until 7pm today, a spokesman for the RBS Group said.
The banking group apologised to customers for the problems, which began yesterday and meant that many people found their balances had not been updated overnight.
The spokesman said: "This is a technical problem affecting a large number of NatWest and Ulster Bank customers, and a small number of RBS customers, including some of our business customers.
"It was caused by a failure of our systems to properly update customers' balances overnight.
"The main problem customers are having is that where people have had money go into their accounts overnight, there may be a delay in it showing up on their balance.
"This is an unacceptable inconvenience for our customers, for which we apologise."
He said the problem would be fixed "as soon as possible" and no customers would be left permanently out of pocket.
The spokesman said: "We will be keeping over 1,000 NatWest branches in all major towns and cities open until 7pm tonight to assist customers who are unable to get to their branch during working hours."
Angry customers vented their frustration on Twitter, with one saying: "I can't access money paid into NatWest today due to tech problem.
"My daughter may lose her school club place if I don't pay. Sort it out!"
Another NatWest customer wrote on the Twitter website that she felt "let down" by the bank as her wages had not yet appeared in her account.
Bob Spearman, from Petworth, West Sussex, told the BBC his tax credit payment had not been paid into his NatWest account.
"We, like many other low-income families, live from week to week and the Child Tax Credit weekly payment is a lifeline on which we rely," he said.
A spokeswoman for UK Payments Administration, which oversees payments generally, said the problem was not a central one and therefore it did not appear to have affected other banks.
But people expecting payments from people or businesses which bank with NatWest and RBS could encounter delays due to the technical issues at their end, she said.
Last week, RBS and NatWest, which has more than 7.5 million personal banking customers, launched a mobile banking app enabling people to take money from an ATM by making a request on their mobile phone.