Thoroughly wash rice and place in a heavy saucepan with water and salt. Bring to a boil and simmer, covered, until tender but not too soft; about 45 minutes. Fluff with a fork and simmer another 5 minutes, uncovered. Drain well.
Wash and trim leeks, leaving some of the green part. Chop leeks and mushrooms and saute in butter in a large saucepan until just tender; about 3 minutes. Stirring with a wooden spoon, sprinkle in flour and cook 1 minute. Slowly add chicken broth, blending well, and then rice. Stir with a whisk until thickened, then blend in cream and sherry. Remove from heat before it comes to a boil. Season with salt and pepper to taste.