UPDATE 25 April: Some customers can now log in to TSB's online banking service, but the bank is restricting the number of people who can log on. It advises customers to: "Please bear with us and keep trying."
However, customers are taking to Twitter to complain that even when they can log on, they are met with 'error messages'.
TSB customers are facing a fifth day of problems accessing their accounts because of IT problems.
Up to 1.9 million TSB customers are still having problems logging into its online service and banking app, since the bank started to move 1.3 billion customer records to a new system on Friday.
TSB's internet banking and mobile banking app was down this morning, with a message saying that it was down for maintenance and that it was "working hard to fix this as soon as possible".
The issues are understood to have started when TSB attempted to switch over from an IT system it had been renting from Lloyds Banking Group to a new one.
TSB told customers services could be affected between 4pm on Friday and 6pm on Sunday. But users were still reporting problems this morning – some five days after the disruption began.
Customers have reported being given access to other people’s bank details and being unable to check their balance or pay bills on time.
Rt Hon. Nicky Morgan MP, chair of the Treasury Committee, has written to Paul Pester, chief executive of TSB, to find out what has gone wrong, the extent of the failure, and how TSB intends to compensate customers who have suffered a breach of potentially highly-sensitive personal data.
Mrs Morgan says: “The reports of unauthorised transactions, access to other customers’ accounts, and failures of in-branch services have all the hallmarks of an IT meltdown.
“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.
“I will be writing to the FCA in due course for their assessment.”
Users took to Twitter this morning to complain about the continuing disruption to TSB’s banking service.
Kevin Rohan says: “It’s absolutely ridiculous that a big company like this can get something so very, very wrong. I’ve banked with TSB for the best part of 15 years, but that might be about to change.”
Anton Woodward adds: “Still no access to my online banking account and the Visa card doesn’t work. Please advise how I am to run my business?”
Tom Tyler says: “Is this the end for TSB? Shocking disregard for customers with no updates from the bank.”
A TSB spokesperson says: “We are currently experiencing large volumes of customers accessing our mobile app and internet banking, which is leading to some intermittent issues with people accessing our services.
“We are really sorry for the inconvenience this is causing our customers and want them to know we are working as hard and as fast as can to resolve this problem.”
The Financial Conduct Authority, which has the power to fine banks for such failings, says it is “aware of the issue”, while Information Commissioner’s Office says it is “making enquiries” about a “potential data breach”.
James Daley, founder of consumer group Fairer Finance, says: "Banks are expected to do better than this and TSB should expect to be on the end of a fine.
"It's particularly disappointing because the bank has been doing a lot of good things, but you can't just get it right 90% of the time and they are going to have to answer some difficult questions.
"It's now about how TSB handles the situation - there is an awful mess to untangle and hopefully it will be proactive in helping those customers who have been affected."
Customers affected by the issues can complain to the bank. Details can be found here.
If you complain to TSB and are unhappy with the outcome, you can ask the Financial Ombudsman Service to look at your case.