The Cheltenham and Gloucester (C&G), owned by Lloyds TSB, is to close a mortgage and customer service centre that employs 350 staff. The site at Tachbook Park, Warwick, was the head office of the former Heart of England Building Society, before it was taken over by the C&G in the 1990s.
The firm said jobs would be moved to India, Scunthorpe and Gloucester, but gave no breakdown of the figures.
Lloyds TSB Group Union (LTU) described the move as "completely unacceptable".
It said it was inevitable there would be hundreds of compulsory redundancies.
Assistant general secretary Steve Tatlow said: "C&G jobs in the UK are to be ditched merely because existing staff can be replaced by staff in India paid a fraction of their salary."
'Competitive environment'
Mike Mitchell, mortgage and customer services director at C&G, said staff at Tachbrook Park would be offered roles at the firm's Gloucester site - about 50 miles away.
He said: "This is not a decision we have made lightly. We aim to manage any reduction in jobs with care and sensitivity through natural staff turnover, transferring and redeploying staff."
He added: "We operate in a fiercely competitive environment and it is vital that we find ways of running our business effectively and competitively."
The wider Lloyds TSB group has already transferred around 2,000 staff to India.