Put the fish into a pan and cover with cold water. Add a bay leaf and bring gently to the boil. Remove from the pan and set aside to cool.
Melt the butter in another pan on a medium-low heat, adding the onion and the leek. Cover and allow to sweat, without colouring, for about 10 minutes until softened. Season with black pepper.
Stir in the potatoes, then pour in the haddock cooking liquor and bring to a simmer.
Break the haddock into flakes, reserving some for the garnish. Lift out a few potatoes and leeks, also for garnish.
Add the milk and half the haddock to the pan, stir then blend.
Season and serve the soup with a garnish of potato, leek and haddock in each bowl, plus a sprinkling of chives.