Cream the butter and sugar together in a mixing bowl until pale and creamy. Gradually mix in alternate spoonfuls of beaten egg and flour until all has been added and the mixture is smooth. Add the baking powder and mashed bananas and mix well.
Spoon the mixture into an 18 x 28 cm (7 x 11 inch) roasting tin lined with nonstick baking paper, and spread the surface level. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 25–30 minutes until well risen, the cake is golden and springs back when gently pressed with a fingertip. Leave to cool in the tin.
Make the frosting. Heat the butter in a small saucepan. Stir in the cocoa powder and cook gently for 1 minute then remove the pan from the heat and mix in the icing sugar. Return to the heat and heat gently, stirring until melted and smooth, adding enough milk to mix to a smooth spreadable icing.
Pour the icing over the top of the cake and spread the surface level with a palette knife. Sprinkle with sugar shapes and sprinkles and leave to cool and harden. Lift the cake out of the tin using the lining paper. Cut into 16 bars and peel off the paper. Store in an airtight tin for up to 3 days.