Board members at TSB have been told by MPs to urgently consider sacking chief executive Paul Pester over major IT problems at the bank.

The powerful Commons Treasury Select Committee said it had “lost confidence” in Mr Pester and warned that if he continued in his position it could “damage trust” in the bank and the rest of the sector.

Mr Pester has “not been straight” with customers at the bank since its online services were plunged into chaos, it said.

In a letter to bank chairman Richard Meddings, the committee 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.”

Mr Pester apologised repeatedly as he appeared before the committee on Wednesday after a difficult first hearing on May 2 during which chair Nicky Morgan described his evidence as “the most staggering example of a chief executive who seems unwilling to realise the scale of the problem that is being faced”.

Up to 1.9 million people using TSB’s digital and mobile banking found themselves locked out of their bank accounts following the migration of data on customers from former owner Lloyds’ IT system to a new one managed by current owner Sabadell.

The committee said it had faced difficulty “obtaining full and frank evidence” about the scale and nature of the problems at the bank.

It raised concerns about the “openness and transparency” of Mr Pester’s evidence.

Mrs Morgan said: “Since the IT problems at TSB began, its public communications have often been complacent and misleading. This tone has been set from the top – by Paul Pester – and whether intentionally or not, he has not been straight with the committee and TSB customers.

“Dr Pester’s statements that ‘everything is running smoothly for the vast majority of our […] customers’ and that ‘there will be no barriers’ to customers switching accounts, and his denial that there were problems on TSB’s fraud reporting line, are all examples of this.

“The Treasury committee, therefore, has lost confidence in Dr Pester’s position as chief executive of TSB, and considers that the TSB board should give serious consideration as to whether his position is sustainable.”

Harry Rose, Which? money editor, said: “TSB’s bosses should be hanging their heads in shame over the way their customers have been treated for the last seven weeks.

“Many will be rightly asking if the current chief executive is the right person to sort out this mess.

“Instead of being upfront about the extent of the crisis, the bank appeared to downplay it and customers have also been exposed to fraud on a staggering scale.

“Anyone unhappy at the way the bank has treated them should vote with their feet and switch to another provider.”