Preheat oven to 190 degrees C. Line a 12 cup muffin pan with paper liners.
In a medium saucepan over medium-low heat, mix cocoa powder, quick-cooking oats, brewed coffee, water, cinnamon, allspice, nutmeg, treacle and butter. Cook and stir until evenly moist and thickened. Cool slightly and pour into a medium bowl.
Beat the egg into the cocoa powder mixture. Mix in flour, digestive biscuits, wheat biscuits, sugar, bran flakes and poppy seeds. Gradually beat in the milk, adding enough to form a smooth batter. Thoroughly beat in baking powder. Fold in apple, sultanas and white chocolate. Scoop into the prepared muffin pan liners.
Bake 30 minutes in the preheated oven, or until a toothpick inserted in the centre of a muffin comes out clean.