Outsourcing firm Capita is set to cut up to 400 jobs across the UK.
Unite said that as part of the company's proposal, Capita would also offshore a significant number of staff to India.
The trade union said it may consider an industrial action ballot, in response to the moves. The staff affected are understood to work on the Prudential, Royal London and Phoenix accounts.
David Fleming, Unite National Officer said members would be "angry and concerned at the prospect of losing their jobs in the current economic climate".
"Capita is a highly profitable company and to treat loyal and highly skilled workers in this way is deplorable."
The company said in a statement that "in order to maintain its competitive position in the marketplace, optimise operational efficiency and maintain and improve service delivery to its clients, Capita's IT services business has concluded that a revised delivery model is necessary".
In January, Unite branded as "callous" a separate move by Capita to relocate around 200 TV Licensing processing jobs. Capita plans to move those jobs from Bristol to Darwen in Lancashire, as well as cutting 40 separate management jobs from field operations across the country, and five from Glasgow. Some of the work will also be outsourced to India.