Scrub the clams under cold water to remove sand. Place in a saucepan, add water and simmer over medium low, covered, about 10 minutes. Remove with a slotted spoon and set aside to cool. Discard any that do not open. Strain the cooking liquid and reserve.
Open the clams over a bowl to catch any juice and remove the flesh. Dice the flesh and add the juice to the reserved cooking liquid.
Place milk in a saucepan and bring to a simmer. Add potatoes and simmer 10 minutes until tender.
Melt butter in a large saucepan over medium heat and cook onion, celery and garlic for about 5 minutes. Stir in flour and about 100ml of the milk the potatoes were cooked in. Mix thoroughly then add remaining milk and potatoes. Add reserved clam liquid and diced clams and simmer 10-15 minutes.
Season with salt and pepper. Serve hot garnished with green onions and smoked salmon.