Customer details are alleged to have been left in insecure bags

The information watchdog, Richard Thomas, told the Times that he had received "highly disturbing evidence".

He is investigating alleged lapses by the Royal Bank of Scotland, Halifax, HSBC, Natwest and Post Office, it said.

The British Bankers Association said it was normal practice to dispose of confidential information securely.

It said this was done using specialist rubbish collection teams.

Mr Thomas told the newspaper he is considering enforcement action which could result in unlimited fines.

He said banks advised people to be careful with personal information and to do things such as shred everything because of identity theft was a "growing problem".

"If the banks themselves are being careless with the information, that seems to me to be wholly unacceptable," he said.

Mr Thomas said among the findings in bin bags were bank statements, loan applications which had been turned down and paying-in slips.

It comes after BBC investigators found customer names, addresses and account details when rifling through discarded rubbish.

The team, from BBC One's Watchdog, warned that the information could be used by criminals to steal clients' identities.