Why wouldn't rabbits be native? It's not so long ago that Great Britain was connected to mainland Europe, so I'd think that most of the same animals would be present both sides of the North Sea.
European Rabbits are native to the iberian peninsula and southern France, they were introduced to the British Isles either by the Romans or the Normans. There's more information about this on the Wikipedia article https://en.m.wikipedia.org/wiki/European_rabbit
