The Financial Conduct Authority said it fined the Royal Bank of Scotland for failing put in place resilient IT systems.
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.
A computer systems failure at RBS, Natwest and Ulster Bank in 2012 affected 6.5 million customers - around 10 percent of the entire UK population.
10% of uk population was hit by the RBS/NatWest computer failure in 2012
The RBS group was today fined £56 million over the crash.
RBS chairman Philip Hampton has apologised to the bank's customers for the "unacceptable weakness" in its IT systems that left many unable to access their accounts.
Our IT failure in the summer of 2012 revealed unacceptable weaknesses in our systems and caused significant stress for many of our customers. I again want to apologise to all customers in the UK and Ireland that we let down.
I am confident that the progress we have made in increasing the resilience of our IT systems.
Natwest and Ulster Bank are among the banks that have been hit with a fine for the Royal Bank of Scotland group over IT failures.
The total fine for RBS - which includes all three banks - is £56 million.
The Royal Bank of Scotland has been fined a total of £56 million by regulators for failings in relation to major IT problems suffered by customers in 2012.
Royal Bank of Scotland has reported third quarter profits of £1.27 billion, compared with a loss of £634 million in the same period last year.
It is the first time the bank has reported a profit for three quarters in a row since the height of the financial crisis, in which the bank nearly collapsed.
RBS also said it was setting aside £400 million to settle foreign exchange rate-rigging allegations.
RBS, which is 80% owned by the taxpayer after being rescued during the financial crisis, said it was putting aside a further £100 million to cover compensation payouts for customers mis-sold payment protection insurance.
Royal Bank of Scotland said it has resolved problems that led to customers being unable to withdraw cash from some ATM machines.
NatWest and RBS customers have been unable to withdraw cash from other than the banks' own cash machines, the bank said.
Customers have taken to Twitter to complain about the problem.
RBS' spokeswoman Nicky Harris said customers should be able to withdraw cash from RBS and NatWest ATMs, but that they are experiencing problems while using other banks' machines.