In reply to Rog Wilko:
What a lot of interesting ideas! We don't ever see a cat in the garden, so probably not that. The rabbit looked very fit and healthy the day before so probably not sick. Never seen a stoat or weasel in the garden, but maybe the most likely.
Still wondering about birds, especially the sparrow hawk. Only seen the male, who I suspect is too small to carry away a rabbit.
My neighbour keeps ferrets, but he keeps them secure. Maybe rabbit could smell them and died of fright.
Post edited at 16:24