IBM/Serco is at the centre of a row over Bradford Council's plans to axe more than 400 jobs.
Public services union Unison said the council had made the decision as a result of "spiralling" computer systems costs.
It said a £110m contract with IBM/Serco had nearly doubled to over £200m in the space of two years.
Unison said it is to ballot members over possible strike action in an attempt to save 408 jobs at the council.
According to Unison, the council is hoping to save £13m as a result of the job cuts.
The union's Bradford branch chair Brian Foster said: "These cuts will have a devastating effect on our members and will be highly damaging to the quality of services to the public.
"We will not stand by and allow these massive cuts to go ahead without giving our members the option to take industrial action".
Neither IBM/Serco nor Bradford Council were available for comment at time of going to press. ®