The Public and Commercial Services union (PCS) said its members had backed walkouts by 91% and other forms of industrial action by 96% in a turnout of 64%.
The union represents 1,600 Driving and Vehicle Standards Agency staff at 360 sites across the UK, including driving examiners and officers who carry out vehicle and traffic safety checks.
The row is over new working patterns, which the union says will lead to longer shifts.
PCS general secretary Mark Serwotka said: “These plans show a blatant disregard for road safety and we’re appalled that DVSA is pressing ahead instead of negotiating with us.”
The union said it will now consider possible dates for industrial action.
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