Staff at one of Brighton's biggest employers fear they could lose their job as bosses look to the developing world for cheaper labour.
Lloyds TSB has launched a pilot project in Bangalore, India, creating 250 posts to work on the Government's Universal Bank Account being introduced next year.
This will involve similar duties already performed by many of the bank's 2,000 strong administrative workforce based in Brighton.
Members of the Lloyds TSB Group Union (LTU) have expressed concern the operation could be expanded at the expense of British workers.
Assistant general secretary Steve Tatlow said: "This type of work has already transferred from branches to service centres so it is not that big a step to transfer it again to the other side of the world.
"It will not see the loss of the tens of thousands of jobs across the country but we are concerned about areas like Brighton, where there are thousands of staff in back office processing."
It is the second time in recent months staff in Brighton have complained about jobs being lost overseas.
American Express, the city's biggest employer, came under fire from employees after setting up a pilot call centre in India.
Labour is a fraction of the cost in the sub-continent - even workers educated to degree level only earn about £4 a day in New Delhi.
Mr Tatlow said: "Lloyds TSB is shortly going to evaluate the success of this project and it would be naive not to think it will have gone well, especially on the grounds of costs, as wages are far lower there.
"We are going to be asking customers outside High Street branches for support and to sign a petition to encourage Lloyds TSB not to go down this road."
However, there was no possibility of strikes among bank staff.
He said: "At the moment, industrial action is not even on our radar. We think the bank will be persuaded to adopt a different policy, especially if we can win customer support."
A spokeswomen for Lloyds TSB said the project in India would only deal with the Universal Bank Account, which would need to be set up by everyone claiming benefit they now receive through the post office.
However, she could offer no guarantees the operation would not be expanded in the future.
She said: "Any moves we make, we consult with the unions and we will continue to work closely with them."
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