Prepare the mussels: discard any broken shells or shells that do not close when tapped. Put the clean mussels into a saucepan and cover tightly. Cook over a medium heat for 4 minutes, shaking the pan occasionally. Check that the mussels have opened – if not, cover and cook for a further 1–2 minutes. Drain the mussels, reserving the juices that have come from the shells. Reserve a few mussels in their shells as a garnish; remove the remainder from their shells and set aside. Discard the shells and any unopened mussels. Rinse the saucepan.
Heat the oil in the clean saucepan. Add the onion, garlic, leeks, celery and carrots and cook gently for 5–10 minutes, stirring frequently, until the vegetables are softened but not browned. Add the potatoes, stock, wine, reserved juices from the mussels, lemon juice, bay leaf, thyme and salt and pepper to taste. Bring to the boil, then reduce the heat to low. Cover the pan and simmer the soup gently for 20–30 minutes or until all the vegetables are tender.
Remove the bay leaf and thyme, then add the shelled mussels, parsley and chives to the pan. Heat gently for about 1 minute. Do not allow the soup to boil or cook for any longer than this or the mussels will become tough and shrink.
Ladle the soup into warm bowls and garnish with the reserved mussels in shells. Serve at once, while piping hot.