Preheat the oven to 170°C.
Place fish in a baking dish, season with salt and pepper and pour over 400ml milk. Cover with foil and bake for 15 minutes until fish flakes away slightly when pressed with a fork. Remove fish, reserving milk. When cool enough to handle, flake fish into bite-sized pieces.
Cook potatoes in boiling salted water until tender. Drain and keep warm. Melt half the butter in a saucepan, stir in flour and cook over low heat for 2-3 minutes.
Slowly add reserved milk and continue to cook until thickened. Add fish, peas, parsley, egg, lemon juice, salt and pepper.
Mash the potato with the remaining 50ml milk and the remaining butter until smooth, then season. Pile the fish mixture into a 1 litre-capacity baking dish, spoon the mash on top and smooth with a spatula. Trace a pattern into the mash with the tines of a fork and sprinkle with grated cheese. Bake for 20-25 minutes until golden.