Abbey's online banking system has suffered technical problems, which meant some users were randomly shown details relating to other customers.
Abbey customers were given a surprise
For example, site users were shown the name of a customer - but it would be displayed with the account details of an entirely different customer.
The bank said there was "no security breach" as the data could not be used to compromise customer accounts.
The problem occurred between 6pm and 11pm on Thursday.
The site was briefly closed for repairs but is now working normally.
Abbey's site problems came to light when customers contacted the BBC News website.
Several readers emailed that they had seen what they thought were personal details of other customers.
"Accessed our account... and got straight into somebody else's account including current, savings and Individual Savings Accounts.
"I was able to access their transaction history, direct debits and could probably have transacted," one emailer wrote.
But an Abbey spokeswoman denied that would-be fraudsters could have taken advantage of the site's technical difficulties.
"There was a short window where customers could view random data, none of which related to a specific customer, and none of which could be transacted on.
"It was a presentational error without any security exposure,
"Our security alerts were triggered and we immediately responded by removing the service to correct the issue," the Abbey spokeswoman said. "Services were fully available by 11pm last night."
The system failure was due to network problems and the bank was looking at ways to prevent a re-occurrence, she added.