To prepare the mussels, scrub and remove the beard. Tap the mussels gently to check to see if they will close. If they do not close when tapped, discard. Discard any that do not open after cooking.
Place the mussels in a saucepan over a medium heat then pour over the white wine. Cover and cook for 5 to 6 minutes, just until the shells pop open. Remove from the heat and discard the shells. Using a slotted spoon remove the mussels from the liquid in the saucepan and set aside.
In the same pan, melt the butter and add the onion, celery, garlic and potato. Cook and stir for 4 to 5 minutes until the onion is soft. Add the bacon and cook for 5 minutes. Sprinkle in the flour then gradually add the milk, stirring constantly until smooth. Add the remainder of the ingredients, except the parsley, and stir well. Simmer gently for 1 hour over a low to medium heat. Just prior to serving, add the mussels back in to the soup and stir well.
Serve hot in warmed bowls and garnish with fresh parsley.