City of London police are investigating claims that an Indian call centre worker sold personal information on 1,000 UK bank accounts for £4.25 each.
The worker told an undercover journalist from The Sun that he could copy more than 200,000 customer accounts a month, containing passwords, addresses, phone numbers and passport details.
More than one bank was thought to be involved in the operation, but the details have been handed to the police.
"It is shocking to see that one individual could get their hands on such complete, confidential information," said Donal Casey, a consultant at IT services company Diagonal Security.
"Quite simply this should not be possible. Banks have multiple layers of security and should be tracking and auditing who, within their organisation and the outsourcer's, has access to and is using confidential customer data."
Many UK firms have moved their call centres offshore in a bid to save money, including most banks, building societies and the National Rail Service. Staff in India cost around 80p per hour compared to £6 in the UK.
The Sun named the seller as Kkaran Bahree and said that he claimed to be able to pass on details of mortgages, medical bills and mobile phones.
He told the journalist that he had a thriving business selling such information to Britain and India, and made contact with buyers via the internet.
"Indian workers are no less ethical than UK workers," said Martyn Hart, chairman of the National Outsourcing Association.
"Companies often assume that, once a process is offshored, minimal management is needed, but this is not the case.
"Because of the distance, increased management is required. This ensures that company procedures are adhered to in every location, not only in Indian locations."