My employer's asked me to drive, but I don't have the correct licence. Am I within my rights to say no?

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.