Beleaguered TSB chief executive Paul Pester found himself under further pressure to keep his job after MPs said they had "lost confidence" in his ability to lead the troubled bank.
In a letter to TSB chairman Richard Meddings, dated June 7 and signed by Treasury select committee chair Nicky Morgan, MPs said: "...the committee considers that the TSB Board should give serious consideration as to whether Dr Pester's position as chief executive of TSB is sustainable.
"The committee has lost confidence in his ability to provide a full and frank assessment of the problems at TSB, and to deal with them in the best interests of its customers.
"It is concerned that, if he continues in his position, this could damage trust not only in TSB, but in the retail banking sector as a whole. I ask that the board consider the committee's view as a matter of urgency."
The letter was issued a day after the TSB bosses were summoned to answer MPs questions on the IT meltdown and the spiralling problems that ensued, and continued long after the bank's failed attempt at migrating its IT systems on 20 April.
It went on to say that parliament was "troubled by the complaints and compensation process, which is not meeting the high standards that you have personally promised the committee".
The letter also criticised TSB's "unsatisfactory public communications since 23 April", after its IT systems, which MPs said compounded the bank's problems.
"These have often been complacent and misleading, and have failed to acknowledge the specific problems faced by customers.
"In this regard, the tone has been set from the top, by your chief executive. Whether intentionally or not, he has not been straight with the committee, and more importantly TSB's customers, about the scale, nature and severity of the problems at TSB, and of the bank's response."
Mr Meddings responded to Mrs Morgan in a matter of hours, saying that the bank's under-fire chief executive "continues to have the full support of the TSB board".
He said: "TSB had made good progress in resolving the recent IT issues and that the banks is now functioning at, or close to, normal for the majority of TSB customers.
"We recognise that we still have areas where we need to improve performance for our customers and we do not underestimate these remaining issues."
Addressing MPs criticism of the bank's inadequate communication after the meltdown, and suggestions that TSB had been misleading, he said: "The board of TSB believes that communications since the migration have been made in good faith, and based on the information available at the time.
As the FCA have themselves noted in their correspondence to the Committee: 'The FCA has no reason at this time to believe that TSB intentionally made misleading or incorrect statements to the committee'."
It emerged during the previous day's hearing that there had been 2,200 attempts at cyber fraud on TSB digital bank accounts following the system failure.
"When he appeared before the committee on 2 May, Dr Pester denied that there were delays or problems on TSB's fraud reporting line, when in fact call volumes, waiting times and abandon rates were far higher than normal.
"No opportunity was taken to correct this in subsequent written evidence of 11 May, despite this containing a section entitled 'Fraud'."
Sky News' Ian King said Nicky Morgan was "essentially calling for his head" and called the letter "extraordinary".
"This is absolutely incendiary stuff," he said.
Mrs Morgan also relayed the committee's lack of confidence in Dr Pester, in letters to Sam Woods, the Bank of England's deputy governor for prudential regulation and Andrew Bailey, chief executive of the Financial Conduct Authority (FCA).
Mr Bailey also appeared before MPs ahead of TSB to give evidence into the TSB debacle.
The FCA is investigating the bank over its handling of the crisis.
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