Definitely. You've not only got a right to refuse to drive a vehicle, but under health and safety legislation you actually have a duty to refuse. Your employer should understand this, and you would certainly be legally protected against any detrimental treatment by your employer as a result of your refusing to drive.
This applies regardless of whether you'd be driving a car or van on the streets, or a specialist vehicle within the workplace or on private grounds.
It is your employer’s responsibility to ensure that you have the correct licence and training for the driving you are doing for work.
