Preheat the oven to 350°F (175°C, 165°C for fan ovens).
Butter an 8 inch round loose-bottom cake pan.
Cream the butter and sugars together in an electric mixer until they are light and fluffy.
Beat the eggs into the creamed mixture.
Sift together the 2 cups flour, baking powder, salt, 1 teaspoon ginger and ½ teaspoon cinnamon.
Add these dry ingredients to the creamed mixture, alternately with the yogurt.
Toss the blackberries in the 1 teaspoon of flour.
Remove the bowl from the mixer and fold the flour tossed berries into the batter very gently using a wooden spoon.
Pour the cake mixture into the prepared pan, coaxing the batter right to the edges of the pan and smoothing the top with a knife.
Core, quarter and thinly slice the apple. (Do not peel.)
Arrange the apple slices on top of the cake in a circular formation.
Combine the demerera sugar and ginger together and sprinkle over top of the apples.
Bake for 25 to 30 minutes or until a skewer inserted in the centre of the cake comes out clean.
Cool the cake in the pan for 20 minutes before carefully removing the sides of the pan and cooling completely on a wire rack. I don't recommend removing the bottom of the cake pan at this stage. (When the cake is absolutely cool, you can or run a knife between the cake and the base and gently slide it off or you can just leave the bottom of the pan on the cake and put the whole thing on a plate to serve.)
When the cake is completely cool, mix together the icing sugar and ginger, and add enough of the water to make a smooth, pourable glaze.
Drizzle over the cake and allow to set before slicing.