Preheat the oven to 180°C (350°F/Gas 4). Grease a 20cm (8inch) round cake tin and line the base with baking paper.
Cream the butter and sugar in a small bowl using electric beaters until light and creamy. Add the egg gradually, beating thoroughly after each addition. Add the vanilla and banana and beat until combined. Transfer to a large bowl.
Dissolve the bicarbonate of soda in the milk. Using a metal spoon, gently fold the sifted flour and mixed spice alternately with the milk into the banana mixture. Stir until all the ingredients are just combined and the mixture is smooth. Spoon into the prepared tin and smooth the surface. Bake for 1 hour, or until a skewer inserted into the centre of the cake comes out clean. Leave in the tin for 10 minutes, then turn out onto a wire rack to cool completely.
Spread the frosting over the cake using a flat-bladed knife and sprinkle with the toasted coconut flakes.