In a large stockpot over medium-high heat, cook bacon until browned. Drain grease. Add butter, onions, and celery to stockpot and cook over medium heat until softened and onions are translucent. Add flour and cook 3 minutes, stirring constantly.
Drain clams and reserve liquid in a 1-pint measuring cup. Add enough water to clam liquid to equal 2 cups.
Add this liquid slowly to mixture in stockpot, stirring constantly. Add potatoes and bring mixture to boil. Reduce heat and simmer about 20 minutes or until potatoes are tender. Add clams, milk and half and half. Heat until thickened, being careful not to boil. Add salt and pepper and serve.