The consumer champion found there were 302 incidents that potentially prevented customers from making payments in the last nine months of 2018.
It said the findings were made by looking at websites and speaking to banks directly in some cases.
It argued the findings highlight the need for a single regulator to be given the statutory duty to protect access to cash and build a sustainable cash infrastructure for the UK, as a “vital back-up” while digital banking is vulnerable to failure.
Since April last year, the Financial Conduct Authority (FCA) has required banks to inform it of operational or security incidents which prevents customers from using payment services.
Which? found the average number of significant breaches across each of the 30 banks and building societies in its analysis was one a month.
It said Barclays reported most major incidents (41), followed by Lloyds Bank (37), Halifax/Bank of Scotland (31), Natwest (26), RBS (21) and Ulster Bank (18).
TSB, whose botched introduction of a new IT system last year caused customers to lose access to online banking services, reported 16 incidents.
Barclays said even minor glitches that have a minimal impact on consumers are reported.
A Barclays spokesman said: “We take IT resilience extremely seriously and we welcome transparency for our customers which is why we report every incident to the regulator, even minor glitches that have minimal impact on customers.
“Our systems are designed to ensure continuity of service for customers in the event of an incident, with a range of channels available to customers including our branch network, telephone, online and mobile banking.”
Which? said it is concerned that more than 25 million people who consider access to cash a necessity risk being left vulnerable without a non-digital payment alternative as bank branches and cashpoints close.
Previous Which? research has found that ATMs vanished at a rate of 488 per month in the second half of last year, while more than 3,300 bank branches have closed since 2015.
Jenny Ross, Which? Money editor, said: “Our research shows that these major banking glitches, which can cause huge stress and inconvenience to those affected, are even more common than we feared.
“This highlights why it is so important that a regulator is given responsibility to protect cash as a backup when technology fails and to ensure no-one is left behind as digital payments become more common.”