Wash and peel the potatoes and cut into slices about half an inch thick. Wash the leeks very thoroughly, as they are often very gritty, trim off most of the green part, and cut the white into thin slices. Melt the butter or dripping in a clean saucepan, put in the potatoes and leeks, and stir them over the fire for a few minutes, taking care they do not brown. Next add the water, a little salt, and about half a teaspoonful of castor sugar. Put the lid on the pan, and let the contents cook until the potatoes are tender, then rub all through a sieve. Rinse out the pan with water, put back the sieved soup, add the milk, and salt and pepper to taste.
Peel the mushrooms, examining them carefully, cut them into neat dice, and stew them in a little milk until they are quite tender.
Re-heat the soup carefully, add the dice of mushrooms, and serve in a hot tureen.
Cost, from 1s. 3d. to 2s., according to season.