Toss the rabbit in the flour to coat evenly, shaking off any excess flour. Heat the oil in a wide, flameproof casserole and cook the rabbit over a moderate heat, turning often, until golden brown. Remove from the pan.
Add the onion to the pan and cook for 2 minutes, then add the mushrooms and cook for a further 2-3 minutes, stirring often. Add the browned rabbit, black pudding, cider and Worcestershire sauce.
Bring to the boil, cover and simmer gently for about 1 hour, stirring occasionally, until the rabbit is tender. Adjust salt and pepper to taste.
Melt the butter and sugar in another pan, then add the apples and cook gently for 2-3 minutes, stirring, until golden. Sprinkle with cider vinegar and bubble for a few seconds. Spoon the apples over the casserole and serve hot, with crusty bread or baked potatoes.