The FCA fined the banks £42m, and the Prudential Regulatory Authority fined them a further £14m.
All three banks are part of the RBS group, which is partly owned by the taxpayer.
The FCA said it has taken this action against the banks for failing to put in place resilient IT systems which could withstand, or minimise the risk of, IT failures.
The actual cause of the IT incident, which occurred in June 2012, was a software compatibility problem.
But the FCA said the underlying cause was the banks’ failure to put in place adequate systems and controls to identify and manage their exposure to IT risks.
The IT failure affected over 6.5m customers in the UK for several weeks.
Customers could not use some online banking facilities or obtain accurate account balances from ATMs.
People were left unable to make timely mortgage payments and without cash in foreign countries.
During that time the banks applied incorrect credit and debit interest to customers’ accounts and produced inaccurate bank statements, leaving some organisations unable to meet their payroll commitments or finalise their audited accounts.
Tracey McDermott, director of enforcement and financial crime at the FCA, said:”Modern banking depends on effective, reliable and resilient IT systems.
“The banks’ failures meant millions of customers were unable to carry out the banking transactions which keep businesses and people’s everyday lives moving.
“The problems arose due to failures at many levels within the RBS Group to identify and manage the risks which can flow from disruptive IT incidents and the result was that RBS customers were left exposed to these risks.
“We expect all firms to focus on how they ensure that they can meet the requirements of their customers when looking at their IT strategies and policies.”