In a saucepan, cover the potatoes with water and bring to a boil. Cook until tender, approximately 15 minutes.
Place halibut and salmon in a skillet with milk. Simmer covered until fish flakes easily with a fork, about 5 minutes based on fillet thickness. Drain milk and set fish aside.
Once the potatoes are cooked, drain them and transfer to a large bowl. Add one egg and butter, and mash until smooth. Season with nutmeg, Worcestershire sauce, salt, and pepper. Gently incorporate the fish, being careful not to break it into small pieces.
Beat the last egg and put on a plate. Spread bread crumbs on a separate plate. Lightly flour your hands and shape the fish mixture into patties. Dip each patty in the egg, then cover with breadcrumbs. Arrange the fish cakes on a plate and chill for 30 minutes.
In a large heavy skillet, heat 1/4 inch of oil over medium to medium-high heat. Fry the fish cakes for 3 minutes per side until they turn golden brown. Drain on paper towels and serve immediately while still hot.