In a scathing letter to the Treasury Select Committee, FCA chief executive Andrew Bailey wrote: "We do not normally make this information [the investigation] public, but, given the level of public interest, I want to be clear that we will be conducting this work."

Bailey was responding to queries from the influential parliamentary committee about the problems faced by retail and business customers following TSB’s IT migration.

Referring to a gruelling Q&A between the bank's boss Paul Pester and MPs in the wake of the meltdown, Bailey says that the TSB chief "was portraying an optimistic view of the services” and that "greater caution would have made sense".

TSB called in a team of fire-fighting consultants from IBM to help fix the problems which saw 1.9 million customers locked out of online and mobile services for over a week. Five weeks have since passed and customers are still complaining about shoddy service standards, security issues and poor communications from the bank.

Bailey agrees: "The FCA has been dissatisfied with TSB’s communications with its customers and we have had concerns that TSB was not being open and transparent about the issues experienced."

He adds that the failings could reduce trust in TSB and "in the banking sector as a whole".

A surge in phishing activity which has seen some customers lose thousands of pounds in the wake of the crisis is also proving a major concern. Says Bailey: "TSB have not met the requirement in the Payment Services Regulations to refund all relevant customers as soon as practicable and in any event by the end of the business day after the day which it becomes aware of the fraud."

Pester is to face another grilling by MPs into the ongoing problems at the bank later today.

Says Committee chair Nicky Morgan: "The regulator does not make such criticisms lightly. I am deeply concerned by TSB’s poor communications about the scale and nature of the problems it has faced; by its response to customer fraud; and by the quality and accuracy of the oral and written evidence provided by Dr Pester to the Committee.

Update: Appearing before the Committee, the FCA's Bailey says TSB is not yet out of the woods: "There are a lot of things going wrong in branches, quite basis and important things. These things still need fixing and it will take time."

On fraud, Bailey says there have been about 10,600 incidents of fraud reported, with customer accounts blocked while the bank investigates. The level of fraud remains on an upward trend and TSB is "struggling to cope".

Pester says the volume of attacks were 70 times the normal level, overwhelming the bank's ability to respond. He says he was shocked at reports of customers waiting up to nine hours to speak to a member of the bank's fraud department and has since installed a dedicated fraud hotline.

Pester refutes the 10,000+ customer fraud figure offered up by Bailey, saying that figure reflect the number of alerts on accounts tracking suspicious activity. Rather 2200 customers had experienced attempts to access their accounts, and 1300 had suffered actual financial losses