A spokesman for eBay said the firm was also looking into what had happened.
"Clearly such details should never have been included in the hard drive of the computer offered for sale on eBay," said the spokesman.
"We fully expect Mr Chapman to hand it back to Graphic Data as soon as possible. We will of course work with Graphic Data to establish how it came to be available for sale on our site."
The Information Commissioner's Office said an investigation would be launched as soon as Mr Chapman had handed the computer in to them.
A spokeswoman said: "We are now investigating this potential data breach and will be seeking an urgent explanation from Graphic Data to establish what has gone wrong and the steps that are being taken to prevent a similar incident occurring."
Banks have an obligation under the Data Protection Act to keep all personal information secure.
Last year the Financial Services Authority fined the Nationwide Building Society £980,000 for a security breach, after a laptop containing customer data was stolen from an employee's home.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.