Lloyds TSB's Fraud Response Team sent letters to some customers in December warning them that they may have been targeted by a Trojan Horse virus after the British bank was alerted by payments association Apacs to the threat.
The letter stated: "Lloyds TSB has been recently advised that your computer may have been infected with a virus. This virus is specifically designed to steal personal information including credit card and your internet login details.
"This virus can be difficult to detect and you may have downloaded this unknowingly. It can compromise your use of the internet banking information on your PC including your Lloyds TSB passwords and memorable information."
However Computer Weekly reports that an IT director, a customer of Lloyds TSB, was angered after contacting the Fraud Response Team, which did not respond fully to his questions.
Although the bank confirmed that security had been breached by his personal details having been published on a now-defunct website, it refused to give any more details.
"You cannot go to a customer and spread panic. You go to them with consolidated information and do not just throw unqualified data at them," the unnamed man said. "They said my details have been published on the internet. I asked what details and where and they could not answer."
"I have asked to be informed about what this personal information was, and so far Lloyds TSB has been far from helpful and have never responded to my calls," he added.