"For instance, customers can check their balance and withdraw money at a cash machine and they can also, as always, do this and make payments through their local Post Office". It coincides with a shift to Banco Sabadell's own banking platform following TSB's £1.7 billion takeover in March 2015, less than two years after TSB was demerged from Lloyds Bank.
On Tuesday the bank's mobile app and online banking platform were taken down for several hours amid a backlash from angry customers.
While access has been restored, the bank has limited access due to the large numbers of users expected to try to log on following the outage.
Morgan said the reports of unauthorised transactions, access to other customers' accounts, and failures of in-branch services "have all the hallmarks of an IT meltdown".
Bank TSB has said its online banking systems were switched back on as of Wednesday morning, following days of problems following on from a botched system switchover at the weekend.
TSB owner Sabadell had initially said the move was a triumph, issuing a statement on Monday on the "successful" completion of the migration according to an archived snapshot of the release on the bank's website seen by Reuters.More news: Manhunt underway for man accused of shooting, killing sheriff's deputy in Maine
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"This is yet another addition to the litany of failures of banking IT systems".
Nicky Morgan MP, chair of the Treasury select committee, said in a letter to Pester: "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". "Potentially millions of customers could be affected by uncertainty and disruption", she said.
"Warm words and platitudes will not suffice".
Banking regulator the Financial Conduct Authority said: "We are aware of the issue and are liaising with the firm".
"From what has happened, it is clear to me that something seriously went wrong with TSB's procedures" on internal system testing, customer communications, information security management and data protection. We both work away from home and heavily rely on internet banking. However, it was forced to take its new system offline for nearly all of Tuesday to implement fixes.