Wash the vegetables. Cut the potatoes, carrots and onion into small cubes and the white part of the leeks and celery - into thin circles. In a pot with a lid, saute the vegetables in the margarine on low heat until tender.
Prepare an aromatic bouquet, by wrapping the bay leaf, bunches of thyme and parsley in a piece of the green part of the leeks. Tie with thread and place it with the vegetables. Add 6 1/5 cups (1.5 liters) of water and after it comes to a boil, reduce the heat. Allow the soup to boil for about 30 minutes.
Remove it from the heat and remove the aromatic bouquet. Beat the boiled vegetables with a blender and strain to produce a fine mixture. Put it in a pot and cook it for another 10 minutes on low heat.
Add the liquid cream and season it with salt and pepper. Serve this soup hot, sprinkled with finely chopped parsley.