Preheat oven to 180 C / Gas 4. Grease a 25cm (10 in) round springform tin and line the base with baking parchment.
For crumble topping, mix demerara sugar, flour and cinnamon in a bowl. Rub in butter and set aside.
Peel and core apples and grate coarsely. Place in a bowl and add cinnamon. Set aside.
Cream butter and caster sugar until light and fluffy. Beat in the eggs one at a time, mixing well after each addition. Sift in half the flour, mix well, and add the remaining flour. Stir until smooth.
Pour half the cake mixture evenly over the base of the cake tin. Spoon the apples on top and scatter over half of the crumble topping. Spread remaining cake mix over crumble and finally top with remaining crumble topping.
Bake for 70 to 80 minutes. Leave to stand in tin for 5 minutes, then carefully remove the sides of the tin and transfer the cake to a wire rack to cool.
You may use desiccated coconut in the crumble topping. If the cake browns too quickly, cover with foil.