Unison says an indicative ballot showed that 97 per cent were prepared to take industrial action, claiming it is the "straw that broke the camel's back."
It came after the council said it was withdrawing passes from 166 casual car users who use their own cars for work.
Unison negotiated the passes in 2012 after staff were relocated into the city centre from outlying centres which had their own car parking space.
Unison branch secretary Adrian Kennett said: "To say this is insensitive is an understatement.
“Local Government workers have had a pay freeze for three years followed by pay rises of between 0.5 per cent and one per cent for the last four years, they have lost onaverage Â£1,600 per year as costs have risen and now the council wants to force them to pay to do their jobs."