everyone I know has been buried or cremated the friday after, be that buried or cremated. So that has been between 3-5 days. With the exception of a friends daughter who died in France and a friend who killed himself, and needed identifying.
i forgot to add, if there is a post mortem examination, it may take longer. I think the difference in the timing is because the vast majority of people in england get cremated rather than burried, so the slots get filled up quickly!