TSB chief executive Paul Pester will give up his “integration bonus” following the IT meltdown at the bank but his full pay and bonus package will not be decided until the end of the year, the Treasury Committee has heard.

Mr Pester told MPs that TSB would “come back” from the issues that have affected the day-to-day banking of thousands of customers, but was told that his performance was “the most staggering example of a chief executive who seems unwilling to realise the scale of the problem that is being faced”.

He was appearing before MPs as the hitches persist for a second week.

He said 40,000 complaints had been received over a 10-day period – and promised they would be put right.

The chaos started following an IT migration, with up to 1.9 million people using TSB’s digital and mobile banking finding themselves locked out of their accounts.

Mr Pester said: “As the chief executive of the bank I absolutely take full responsibility for what has happened with TSB through this migration.”

Asked if he had failed in the basic duty of a bank to let customers put money in, take money out and keep money safe and secure, Mr Pester said: “I feel we have failed in delivering the level of service we need to deliver to our customers, clearly.

“TSB was built to bring local banking to Britain. TSB was built to reconnect banks to local  communities.”

He continued: “I’m deeply sad that the work we have done over the last five years in building TSB as a different sort of bank has been so damaged over the last 10 days.

“But we will come back as TSB. TSB will come back and bring the competition it needs to bring to UK banking.”

TSB chairman Richard Meddings said Mr Pester would not be taking his bonus for the integration, adding that this was “wholly appropriate”, but said his bonus in its entirety would be assessed at the end of the year following the outcome of an independent review.

Mr Pester, along with Meddings and Miquel Montes, chief operations officer at TSB’s owner, Sabadell, faced questions from a group of MPs led by Nicky Morgan, who at one point said: “What we are hearing this afternoon is the most staggering example of a chief executive who seems unwilling to realise the scale of the problem that is being faced.”

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Earlier during the hearing, Mr Pester said: “You will be aware that the source of these issues was a migration that we did the weekend of April 21 and 22 and over that weekend we extracted all of our customer records for 5.2 million customers – 1.3 billion records – transformed those records and loaded them on to a new platform.

“I’m certainly not downplaying anything about the issues that our customers have faced since then but it’s important to understand that that migration of data went smoothly, the bank balanced to the penny, so the £31 billion worth of customer balances from Lloyds have come across to the new platform and the balances are balanced to the penny.

“The underlying engine of the bank is actually running relatively smoothly.

“The issues that we are seeing, for which I apologise again to our customers, is that the platform’s ability to support sufficient customers accessing our website and mobile app simultaneously was an issue for us Monday, Tuesday, Wednesday last week.”

He said about 95% of customers were now having success accessing the bank’s internet and mobile services, adding: “We did not see those figures soon after the migration and, as I say, that led to an unacceptable level of performance to our customers.”

However he struck a sour note when, in response to Ms Morgan telling him that two members of staff were unable to access TSB’s mobile app as the hearing was going on, joked: “It’s nice to know there are so many customers in the room. Thank you very much for using TSB.”

Asked when the “shambles” would be over, Mr Pester said: “Clearly I’ve misled you if you think that I’ve said that this bank is fixed.

“I can’t give you a fixed date. If I give you a fixed date it is likely to be unfair to our customers. We are working hard on fixing the middleware issues we have described.

“We expect to see the service improve but I can’t give you a date because I don’t want to mislead our customers.”