Lloyds TSB could face a legal challenge over the transfer of sensitive personal information to processing centres in India without a customer's consent.
Outsourcing abroad may mean breaking UK laws, unions claim
The bank's trade union is examining whether to mount a civil court challenge to the practice
An unnamed customer is also considering similar action.
Law firm Bindmans - which is handling both cases - argues that laws governing data protection in India are not as stringent as those required in the UK.
Under European law, sensitive personal data can only be transferred outside the European Economic Area with the express consent of a customer.
Lloyds TSB union claims that the action is an "important case" which could force the bank to drop its offshoring policy.
So far, it has referred its concerns to the Information Commissioner to discover whether Lloyds is living up to its Data Protection Act duties.
"If successful, this case could force Lloyds TSB to obtain the written consent of customers before transferring their sensitive personal information abroad," the union said.
"Since there is a considerable body of research indicating just how unpopular offshoring is amongst customers, this could force Lloyds TSB into rethinking its whole 'Jobs to India' strategy."
However, Lloyds denied it had breached any EU or UK laws.
"Security is of the utmost importance to us," it 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."
Under its off-shoring plans, Lloyds aims to have 1,500 workers in India by the end of the year.
Outsourcing jobs abroad can offer huge savings to companies - and financial services firms have led the exodus from the UK.
In India, UK banks can cut costs by paying graduates as little as $200 a month to work in administration and answer customer calls.