Computer giant Hewlett Packard (HP), which has the contract to maintain the records of millions of people for the Department for Work and Pensions (DWP), has begun consulting over its plans to relocate up to 200 jobs overseas.
No final decision has been made as the plans are subject to approval by the DWP and the Cabinet Office for security reasons.
The Public and Commercial Services (PCS) union urged the government to intervene to prevent the jobs being moved abroad.
PCS members employed by HP on the government contract voted almost unanimously for action short of a strike over concerns for their jobs and the security of the information.
The industrial action means staff will refuse to co-operate with the process of exporting their work from sites in Newcastle, Lytham and Sheffield to Bangalore.
The union said that if the move goes ahead it could set a precedent as contracts do not forbid the transfer of government IT work overseas.