Rub a little of the butter all over the base and sides of a cooking dish and stand the dish on a baking sheet. Put the butter, sugar and eggs in a large bowl and sift in the flour, cocoa powder and baking powder. Beat together with a wooden spoon until they form a smooth mixture. Spoon the pudding mixture into the dish and spread the top level.
Put the cocoa and sugar for the sauce into a small bowl and mix in a little of the measurement boiling water to make a smooth paste. Gradually mix in the rest of the water, then pour the cocoa sauce over the pudding mixture.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 15 minutes or until the sauce has sunk to the bottom of the dish and the pudding is well risen. Sift a little icing sugar over the pudding and serve with scoops of vanilla ice cream or a little pouring cream.