For the apples, peel, core and chop the cooking apple into 1cm cubes. Place the apple, sugar and water in a small saucepan and cook on the hob on a medium heat for 5 minutes or until soft. Turn off the heat and put to one side.
For the sponge, lightly grease the pudding bowl or basin with a little butter or margarine. Place the sugar and butter or margarine into a large mixing bowl and beat until light and fluffy.
Add the eggs one at a time, beating well to combine before adding the next. Gently fold in the flour. Carefully stir the cooked apple and blackberries into the sponge mixture. Transfer the mixture to the pudding bowl and spread evenly with the spatula. Cover loosely with a lid or cling film, making sure that it is not touching the sponge mixture. Place the pudding in the microwave on a high setting for approximately 6 minutes (this may vary slightly depending on the power of your microwave). The sponge should rise and be firm to the touch. Leave to stand for 4–5 minutes before turning out onto a serving plate. Serve on its own, with custard or yoghurt.