Melt the butter in a saucepan over a medium heat, then add the onion and fry for 5-8 mins until translucent but not browned. Add the potatoes and 300ml water and bring to the boil. Reduce the heat slightly and simmer for 10-15 mins.
Meanwhile, put the haddock in another pan and cover with the the milk. Cook gently for 5 mins, or until just tender. Remove the haddock from the milk with a slotted spoon (reserving the milk), transfer to a plate and leave to cool slightly. When cool enough to touch, flake into large pieces, removing any bones.
Put the reserved milk and flaked haddock in the pan with the potato mixture and cook for another 5 mins. Season and sprinkle over the parsley to serve.