Here in Scotland, the law is clear. If the sheep was on fenced land, and it gets onto a road, the farmer is responsible. If the sheep was on unfenced land, (and there are a lot of sheep on a lot of unfenced land in Scotland), the motorist is responsible. (Tip. If you come across a lamb on one side of the road, and a ewe on the other side of the road, then slow down or stop, because it's a 100% certainty the lamb will dash back to its mum right in front of you at the last instant).
(Another tip for Scotland. If you kill a deer, or come across a dead one, don't touch it - report it to the police. If the police find anyone carrying a dead deer they will be automatically suspected of poaching, and the penalties for that are pretty severe. You would likely be taken to the local lockup, and held there while a vet carries out a post-mortem to determine whether the animal has been shot. And the vet may not appear till next day if he's called out of normal working hours!)