Melt the butter in a heavy saucepan. Add the carrots and onions, and sweat until soft.
Add the potatoes and tomatoes, and season with salt and pepper.
Pour in enough water to come to just below the top layer of tomatoes and bring to the boil. Boil slowly for 20 minutes.
Mix the flour and milk together until smooth, and stir into the stew. Lay the cod on top of the stew, and cook for 10–20 minutes. Serve hot.