LLOYDS TSB could face legal action over plans to move its call centre operations to India.
The trade union representing bank workers is considering the challenge under the Data Protection Act.
Lloyds announced last year it was shedding nearly 1,000 jobs at its Newcastle call centre and moving the work to India.
The Lloyds TSB Group Union says a customer has lodged a complaint that sensitive personal data may not be subject to the same stringent data protection laws if it is handled outside the European Economic Area.
Judy Baker, associate at North-East law firm Ward Hadaway, said there was nothing in UK law to prevent Lloyds TSB from offshoring.
She said: "But the legislation does put heavyweight obligations on any company wanting to send personal data offshore.
"It may have to obtain the explicit or unambiguous consent of its customers to the offshoring, for example.
"However, UK data protection laws are complex, and it is often possible to find alternative ways of complying with those laws to achieve a desired end. Whether Lloyds TSB can do that here, remains to be seen."
If the legal challenge is successful, the move could force other banks to review their decisions to send processing work offshore.
A Lloyds TSB spokesman said: "We are confident that we comply with the Data Protection Act and our customers can be reassured that their personal information is as protected in India as it would be in the UK."
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