HMRC, the Office of National Statistics and the DVLA could be affected as PCS union members at Fujitsu vote in favour of strike action.
Of 720 members 65% voted for a strike, and 85% for other forms of industrial action. There was a 63% turnout. Strikes could now take place in September and October.
The industrial relations issue has come after continued dissatisfaction over the treatment of a Unite union member Alan Jenney.
Workers feel he was unfairly dismissed by Fujitsu due to his position as a union rep. During headcount cuts at Fujitsu, other staff members were redeployed. Workers feel Mr Jenny was unfairly targeted by management.