Spanish banking giant Santander has sent bank statements for up to 35,000 customers to the wrong addresses.
The group said a printing glitch led to customers being sent the first page of their own bank statement but pages two and three of another customer's.
The statements included customers' names, account numbers and details of transactions they had carried out, although Santander insisted this was not enough information to enable someone to commit fraud on their account.
Despite this, it has written to all affected customers informing them of what has happened, and informed City watchdog the Financial Services Authority about the problem.
It has also warned all of its branch and call centre staff not to reveal account information to anyone without taking them through the full security procedure, which includes people having to give extra information, such as their mother's maiden name.
A Santander spokesman said: "Due to a technical error at our printer's, a number of current account statements dated December 18 have printed incorrectly.
"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 incident 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 group said none of the bank statements that were sent to the wrong address contained information on customers' addresses.
But MoneySavingExpert.com said one of its users has claimed he received someone else's statement and could see their name, address, account details and recent transactions.
Martin Lewis, creator of MoneySavingExpert.com, said: "Someone needs to grab hold of the reins at Santander. The bank is continually coming bottom in customer service surveys and this is yet another example why. The thing people need most from their bank account is trust it'll be secure - sending statements to the wrong people doesn't do that."