The software problems, which left many customers unable to pay bills, access their accounts and even receive their wages, have now been fixed but staff are now battling a huge backlog of unprocessed transactions.

A spokesman for Royal Bank of Scotland (RBS), which owns the other two banks, told AFP a "large majority" of the trio's combined 15 million personal banking customers had been affected by the IT meltdown.

RBS chief executive Stephen Hester issued a public apology on Saturday and admitted that customers had been let down.

"I am very sorry for the difficulties people are experiencing," he said. "Our customers rely on us day in and day out to get things right, and on this occasion we have let them down. This should not have happened.

"Right now my top priority, and the priority of the entire RBS Group, is to fix these problems and put things right for our customers.

"This is taking time, but I want to reassure people that we are working around the clock to resolve these problems as quickly as we are able."

Hester said double the usual number of staff were manning call centres to tackle the problem, which reportedly arose after a failed attempt to install an update on RBS's payment processing software.

RBS and NatWest branches were to open on Sunday between 9:00 am (0800 GMT) and 12:00 pm, while Ulster Bank branches would stay open until 1:00 pm.