Heat the oil in a large, deep-frying pan. Add the chipolatas, cook until brown all over, then push to one side of the pan. Add the bacon to one part of the pan and the mushrooms to the other. Fry until the bacon starts to crisp and the mushrooms are golden. Tip the contents of the pan onto a plate.
Tip the beans, passata and tomatoes into the frying pan. Add the ketchup and chilli (if using), and season well. Bubble for 5 mins, then scatter the mushrooms over the top and nestle the chipolatas and bacon among the beans. Create two to four gaps in the beans (so you can see the base of the pan) and crack in the eggs. Cover the pan with a lid or baking tray and cook for 4-5 mins until the egg whites are cooked through but the yolks are still runny. Scatter with parsley and extra chilli, if you like, and serve with hot buttered toast.