Financial regulators and politicians will take a tougher line on banks over IT failures because branch closures have forced customers to move online, Treasury committee chairwoman Nicky Morgan said.
The senior Tory MP said being left without internet banking access was as disruptive as "turning on the tap and not getting any water" for consumers.
And she also warned firms they must take extra action to ensure customers' personal information is protected.
At a speech to City leaders, she said: "The shift online has led to heightened customer expectation about service level availability, particularly in banking.
"Finding oneself locked out of online banking is fast becoming equivalent to turning on the tap and not getting any water.
"So as firms use the availability of online banking as a reason to close branches, the committee and regulators will rightly become less tolerant of IT failures for the quite simple reason: The detriment caused to consumers is greater than ever."
She told the TheCityUK conference in London that the troubles with TSB's online systems and the Facebook data scandal illustrated concerns over the handling of personal information.
"The Facebook and Cambridge Analytica scandal has caused a breakdown of trust between consumers and firms that hold their data," she said.
"The financial services industry has to look closely at lessons from the the industry where customers, through their data, have become the product.
"And it has to uphold the highest standards of care and stewardship of personal information.
"The industry cannot afford to lose the trust of customers through data breaches or mishandling of customer data."
She said the TSB situation "perfectly illustrated how botched IT projects can create a goldmine for fraudsters".
Mrs Morgan also stressed that as more and more customers moved online, banks had to ensure that non-digital customers and cash users "must not be left behind".