Problems at TSB are well into a fourth week, with the bank being accused of a "dreadful response" at the outset of its IT crisis.
Philip Augur, a former TSB board member, said "human error, pride and software failure" led to a disaster.
Some customers are still struggling to make payments, particularly from business accounts, and mortgage accounts cannot be viewed online.
TSB says it is working around the clock to solve the problems.
Speaking on Radio 5 live's Wake Up to Money, Mr Augur, now an independent banking commentator, said that TSB "clearly underestimated the gravity of this in the early days" and the response to the crisis in the first week was "dreadful".
The migration of data on TSB's five million customers from former owner Lloyds' IT system to a new one managed by current Spanish owner Sabadell created major difficulties for the bank, which has received more than 40,000 customer complaints so far.
Midway through the week after the migration, experts from computing giant IBM were called in by TSB.
Significant frustration from customers remains despite some improvement in the subsequent weeks, including to online and app access.
The frustration is caused not only by the IT problems, but also by long waits for help on TSB's phone line. Mr Augur argued that helpline staffing should have been a greater part of planning before the migration.
The bank has repeated a previous promise that no customers will be left out of pocket as a result of the problems.
"Our teams have continued to work around the clock to put things right for our customers. Our website and mobile banking services are operating at around the same levels that they were prior to the system change," a spokeswoman said.
"We are working with experts from IBM to resolve the remaining issues, and our focus is on getting everything back to normal for our customers as soon as possible."