Combine water, potatoes, carrots, celery, and 1/2 teaspoon salt in a medium saucepan. Bring to a boil. Reduce heat; cover and simmer 15 minutes. Set aside.
Sauté onion in butter in a large Dutch oven until tender. Add fish and Worcestershire sauce; cook over medium heat 1 minute, stirring gently. Add cooked vegetables and liquid, remaining salt, and pepper. Cover and simmer 10 minutes.
Gradually stir milk into flour, blending until smooth. Stir milk mixture into fish mixture. Cook over low heat 15 minutes or until thoroughly heated. (Do not boil.) Spoon chowder into individual serving bowls; sprinkle with paprika.