Lloyds TSB is shedding about 150 posts as it moves more work to India.
Lloyds TSB said all those affected will be offered other jobs
The bank is outsourcing administration roles to the firm Xansa, based at Noida in the state of Uttar Pradesh.
Union leaders have condemned the move, but Lloyds TSB says all those affected will be guaranteed the offer of another job at Lloyds TSB.
Bristol will lose 83 jobs, Cardiff 21, and 20 each are going at Mold, Flintshire, and Telford. The changes will be made over the next 12 months.
Lloyds TSB hopes the outsourcing will improve the technology used in administration and allow a better support service for staff.
The Lloyds TSB Group Union (LTU) claims staff will receive an inferior service on key issues.
Steve Tatlow, Assistant General Secretary at the LTU, said: "Lloyds TSB is showing the same contempt to its staff as it is already inflicting upon customers, through placing cost-cutting ahead of any service quality considerations."
In a statement, Lloyds TSB said: "We maintain the same high standards of customer services (in India) as we do in the UK. In 2005 we recorded our highest ever customer satisfaction scores across all our channels."
The bank added its off-shoring job security agreement, which includes the offer of a training bond of up to £2,000 towards the cost of recognised training courses, will help those who choose to leave.
Bernard O'Driscoll, HR Services director at Lloyds TSB, said: "We will be talking to all staff individually over the next few weeks to discuss how this decision affects them and what their preferences are for the future."
The bank plans to cut its back office costs by £121m a year by 2010. The wider group has already transferred some 2,000 jobs abroad.