Over 160 Steria employees working for the Identity and Passport Service are to strike over poor pay.
Some Steria employees are paid as little as £13,500 a year and are threatening further action in August if necessary, said the Public and Commercial Services union.
Profits at French IT services company Steria rose dramatically last year, up €9.3 to €25.2m, from €15.9m in 2009.
The Public and Commercial Services union (PCS) said the strike action would delay applications for new or renewed passports at the busiest time of the year for the Identity and Passport Service (IPS).
Previously staff had rejected a pay freeze for those on £21,000 a year and above. All other employees will receive on average around £180 pro rata over a nine-month period. The PCS members voted 86% in favour of strike action and 90% in favour of action short of a strike.
PCS general secretary Mark Serwotka said: "These private sector staff provide an invaluable public service for UK citizens applying for or renewing their passports.
"Yet instead of rewarding its workforce with a decent pay rise, the company is imposing what is nothing more than a pay cut at the same time as pocketing millions in profits."
Steria was unavailable for comment on the strike action.