It will depend whether the road is adopted by the council, who owns it and who is responsible for maintaining it.
I think I have heard that it is illegal to permit rainwater to run off (drain) one property to the detriment of another owned by someone else.
In thsi case, you should seek legal advice and if the council is responsible submit a claim for the damage the water has caused your driveway.
Bear in mind though, that we have had some quite exceptional wet weather this winter.