Actually, a little of both; warming and cooling. Seems there used to be a land bridge between the continent and Britain (kinda like the one that used to be between Alaska and Siberia) long, long ago. But subsequent cooling massed ice up against it, and warming flooded it, eroding it away over time.
Or at least that was the theory postulated on the History channel show I saw a few weeks back. I forget which show.
This discovery would seem to validate the theory.