Staff at EDS, who are now employed by HP, are voting in a strike ballot as they express their "anger" over upcoming job losses.
Most of the 1,000 staff, who are members of the PCS union, work on a series of IT contracts at the Department for Work and Pensions that are worth £3 billion (US$5 billion) and run until 2015.
They work in locations around the UK, including Newcastle, Washington, Preston and the Fylde Coast, on areas including desktop and datacentre management, and application maintenance and support.
There had been "growing anger" among the staff since HP bought EDS in 2008, the union said. Their complaint centres on the 1,000 job losses planned for the first half of next year, as well as a pay freeze, a growing workload, and voluntary salary cuts.
Some 3,400 staff have already been made redundant since the takeover.
The PCS ballot offers staff the chance to vote on a series of strikes of one or two days, as well as action that falls short of a strike. Staff have until 30 November to vote.
"There has been growing anger amongst staff who are facing yet more uncertainty about their future," Mark Serwotka, PCS general secretary, said.
While employees had been "contributing significantly to HP's revenue" and taking on more work, "their reward is more job cuts, imposed pay freezes and pleas from the company to take a voluntary pay cut", he said.
Serwotka urged HP workers to tell their managers that "enough is enough".
In a statement, HP said it "respects the rights of its employees" to be part of a union and would continue dialogue with the aim of avoiding a strike.
HP is facing a stike ballot on another front, regarding 150 of its service engineers, who mainly work from home and in the field. Those workers are complaining of a reduction of pay and benefits, and the result of their vote is expected in the next few days.
Elsewhere, rival Fujitsu narrowly avoided a three day strike last week, after the Unite union said there had been some progress in discussions on pay and job cuts. But the situation is not resolved and the union did not rule out further strike action.