Heat the oven to 180 C / 350 F. Butter a 20 cm / 8-inch baking dish (1.5 L capacity).
In an 18 cm / 7-inch saucepan, combine the Bramley or other tart baking apples, peeled, cored and sliced 1 cm thick, with the caster sugar, lemon juice, and water. Cook over medium heat for 3 to 4 minutes, stirring, until the apples begin to soften but still hold their shape.
Spoon the warm apples into the baking dish and spread into an even layer.
In a mixing bowl, beat the butter and sugar with a hand mixer for about 3 minutes until pale and fluffy.
Add the eggs one at a time, beating well after each, then mix in the vanilla extract.
Sift in the self-raising flour and salt, folding gently with a wooden spoon until just combined. Stir in the milk to loosen the batter to a soft, dropping consistency.
Spoon the sponge batter over the apples in dollops, spreading gently to cover the fruit without pressing down.
Sprinkle the demerara sugar evenly over the top.
Bake for 35 to 40 minutes until the sponge is golden brown and a skewer inserted into the center comes out clean.
Rest for 5 minutes, then serve warm with custard.