Chop up the apples into roughly 2.5cm (1″) cubes. Set aside.
In a large bowl, mix together the flour, baking powder and mixed spice.
Add the soft butter, and using your fingertips, lightly mix in the butter and the flour mix until you get a coarse, wet sand sort of mixture. Like making a crumble. If you prefer, you could do this part in a food processor, then transfer everything into the bowl to move on to the next step.
Stir in the sugar with a wooden spoon.
Toss in the apples and lightly mix with the wooden spoon.
Slowly add the buttermilk and stir to mix thoroughly.
Tip into your prepared cake tin and sprinkle the demerara sugar all over.
Bake for 50-60 minutes, until a skewer inserted in the middle comes out clean. Eggless cakes always need a little longer than you think.
Serve as suggested. Will keep for 3-4 days, stored in an airtight container.