The boss of TSB has apologised for IT issues which left online customers unable to access their money and some able to see other people’s accounts.

Paul Pester said he was “deeply sorry” for the problems as data and banking watchdogs confirmed they were looking into the situation.

Customers complained of problems with mobile and online accounts several hours after a system upgrade was supposed to have been completed on Sunday.

One customer said they had “access” to other customers’ accounts totalling more than £20,000 and another reportedly discovered they had been credited with £13,000 after logging back in.

A number of customers complained that they were still unable to access their money on Monday morning.

Mr Pester said the systems had been taken offline again to enable further work and promised that no customers would be left “out of pocket” as a result of the problems.

The Information Commissioner’s Office, which monitors data and privacy, said: “We are aware of a potential data breach in relation to TSB and are making inquiries.”

Banking regulator the Financial Conduct Authority said: “We are aware of the issue and are liaising with the firm.”

MPs demanded answers from the bank about the IT meltdown.

Treasury Select Committee chairwoman Nicky Morgan wrote to Mr Pester asking for details of the problems and the bank’s response.

She said: “This is yet another addition to the litany of failures of banking IT systems.

“Potentially millions of customers could be affected by uncertainty and disruption.

“It simply isn’t good enough to expose customers to IT failures, including delays in paying bills and an inability to access their own money.

“Warm words and platitudes will not suffice. TSB customers deserve to know what has happened, when normal services will resume, and how they can expect to be compensated.”

TSB said a “tiny fraction” of customers saw accounts belonging to other customers and the issue was resolved in about 20 minutes.

The bank had told its account holders that some of its services, including online banking, making payments or transferring money, would not be possible over the weekend.

The upgrade window was scheduled between Friday at 4pm and Sunday at 6pm.

TSB’s social media team faced a stream of complaints from customers, including several who said they could see other people’s accounts after logging back in on Sunday evening.

Craig Malcom tweeted: “@TSB I currently have access to £20k+ of other peoples money.

“This is a MASSIVE breach of data protection! If i have access to their account they could have to mine as well!”

Another Twitter user called Bex said: “@TSB so go to my app and have someone else’s accounts there!!!! Serious dpa (Data Protection Act) breach! Want to speak to someone now and a half an hour wait!! What would the FCA (Financial Conduct Authority) say about this!!! Might just inform them a bank is giving away other people’s account numbers”.

Laim McKenzie, from Paisley in Scotland, told the BBC he had been unexpectedly credited with thousands of pounds after logging back in after 6pm on Sunday.

“My balance, because of my overdraft, is in minus, but my balance was showing at £13,000,” he said.