In a large flameproof casserole or stockpot with a lid, place the shallot, white wine, thyme, bay leaf and mussels. Bring to a boil over high heat. Reduce the heat and simmer, covered, for about 2 - 3 minutes, stirring gently once or twice. Discard any unopened mussels. Remove the mussels and set aside to cool, saving the cooking liquid.
Bring the cooking liquid from the mussels to a simmer and add the shrimp, stir, then add the scallops. Cover and cook gently for 2 - 3 minutes, or until firm. Remove from the cooking liquid and set aside.
Bring the cooking liquid back to a simmer and repeat with the fish, poaching for 5 minutes, or until firm. Test the fish by breaking a piece in half to see that it is cooked through.
Remove the mussels from their shells and discard the shells.
Strain the cooking liquid through cheesecloth or a fine sieve to remove any sand.
Place in a saucepan and bring to a boil. Add the mushrooms and cook until all the liquid has evaporated.
Stir in the cream and boil for about 5 minutes, or until it is thick enough to coat the back of a spoon, then add the mussels, shrimp, scallops and fish and simmer until hot.
Season with salt and freshly ground black pepper and gently stir in the parsley before serving.