The High Street bank Santander has blamed printers for a blunder that saw it send 35,000 bank statements to the wrong addresses.
It has written to customers to warn them, but played down potential security problems.
"Due to a technical error at our printers, a number of current account statements dated December 18 have printed incorrectly," the banks said.
"We are sorry for any inconvenience this has caused and have taken immediate steps to correct this. We take the security of customer and account information extremely seriously so any incidents of this nature is treated with the highest priority.
"We want to reassure customers that the risk of fraud on their account has not been increased because of this error and that this is a one-off incident."
The Information Commissioner's Office said: "We have recently been informed of a data breach involving Santander. We will be making enquiries into the circumstances of the apparent breach of the Data Protection Act before deciding what action, if any, needs to be taken."
It was recently granted new powers to fine firms up to £500,000 for data breaches. Financial services firms can also be punished by the more toothy Financial Services Authority. In August it fined the insurance group Zurich more than £2m for losing customers' details. ®