Anthony Browne, chief executive of the BBA, said banks were spending billions of pounds a year upgrading their systems as the rapid growth of digital banking had transformed the way people dealt with their banks.
NatWest owner Royal Bank of Scotland has faced a barrage of customer complaints after admitting yesterday that around 600,000 delayed banking payments may not show up in accounts until the weekend.
RBS said it was working “flat out” to get people’s payments to them.
Asked by BBC Radio 5 Live’s Wake Up to Money programme about the RBS incident, Mr Browne said: “Well it is unacceptable and I mean RBS made clear yesterday it was unacceptable.
“The banks are all very aware of this as an issue.
“A lot of them have creaking IT systems. They are spending £3 billion a year upgrading their IT systems.
“It is one of the biggest IT upgrades that Britain has ever seen, partly driven by the rise in mobile phone digital banking.
“Mobile phones are now the most popular way to contact your bank ... it is exploding.”
Mr Browne said the incident showed how people’s expectations of banks had changed.
He said: “We expect to be in contact with them 24 hours a day, seven days a week.
“We expect real time payments. 97 per cent of payments are now basically real time, instantaneous.”
Mr Browne said the use of IT systems had increased “dramatically” due to surging numbers of people taking up digital banking in recent years - and the industry was “working hard”.
He continued: “We have a far more efficient, effective banking system now than we had a few years ago but the IT systems do have to be upgraded to keep pace with that.”
Taxpayer-backed RBS said yesterday that payments and direct debits had been affected for some customers across all four of its banking brands - NatWest, RBS, Ulster Bank and private bank Coutts.
The issue also affected some Bacs payments, such as tax credits and disability living allowances.
RBS said it had identified and fixed the issue that caused the glitch, but said affected customers may have to wait until Saturday for payments to go through.
There were reports of customers complaining that they had had to put off their food shopping or were struggling to pay household bills as a result of the latest hitch.
The glitch came just days after the Nationwide building society suffered an IT blackout, with thousands of customers left unable to use its full services for two hours on Monday morning.
NatWest and RBS have been hit by a number of embarrassing IT glitches in recent years.
In 2013, RBS’s online service was disrupted by a denial-of-service attack.
Last November, the state-backed group was hit with a £56 million fine from the Bank of England and City watchdog the Financial Conduct Authority (FCA) after a computer failure in 2012 saw as many as 6.5 million customers unable to make payments for as long as three weeks.
RBS has stressed that payments were delayed rather than missing and promised customers they would not be left out of pocket by the latest system error.
Andrew Tyrie, chairman of the Treasury Select Committee, said yesterday: “This looks like a serious IT failure at RBS, the latest of many in the industry.”
He confirmed that he would write to RBS boss Ross McEwan and regulators for “reassurance that the steps necessary to bring a halt to these failures are being taken”.