NatWest, Virgin Money and Bank of Ireland also received letters from the Competition and Markets Authority over regulation failures.
Monzo has been issued with a formal warning after breaching banking rules by not providing bank statements to 143,000 former customers.
The Competition and Markets Authority (CMA) has also written to Bank of Ireland NatWest and Virgin Money reminding them of banking rules which state that any customer or small business closing an account must have a full transactions history provided within 40 days of leaving.
Investigators told the financial institutions that transaction histories must be sent to at least 95% of such customers within 10 working days and future breaches could lead to legally binding extra training or additional oversight by the watchdog.
The rules were introduced in 2017 as part of a push to make switching current accounts easier, while ensuring that customers can still access banking history – a key requirement for credit lenders.
In total, nearly 150,000 customers were not provided with their transaction history – the vast majority with Monzo – with some delayed by a few weeks and others by more than a year, the CMA said.
Adam Land, CMA senior director of remedies, business and financial analysis, said: “This may have made things harder for people trying to borrow money or apply for a mortgage.
“The CMA’s work in the sector is making it easier for people to get a better deal from their bank. Banks must comply with all the rules – that includes providing a full transaction history promptly.
“We will be watching closely to make sure these leading names stick to their word and don’t let their customers down again.”
“The Bank of Ireland, Monzo, NatWest Group, and Virgin Money should be in no doubt that the CMA stands ready to take further action if these failures are repeated.”