Scrub the mussels in a large bowl of cold water, removing the beards and any barnacles. Discard any with broken shells or any that don’t close tight when tapped on a hard surface.
Heat the oil in a large saucepan over a medium heat. Add the onion, bay leaf and thyme and cook for 4 minutes. Stir in the garlic and cook for a further minute.
Pour over the wine and simmer for 1 minute. Tip in the mussels then cover and steam for 3-4 minutes or until all the mussels have opened, shaking the pan every now and then. Discard any that stay shut.
Stir in the cream and chopped parsley and serve in warm bowls with the bread and lemon wedges.