1. Preheat the oven to moderate 180°C (350°F/Gas 4). Lightly grease a deep 20 cm (8 inch) round cake tin and line with baking paper.
2. Sift the flour into a large bowl and add the coconut, lemon rind, sugar, butter, eggs and milk. Mix well with a wooden spoon until smooth. Pour into the tin and smooth the surface. Bake for 40 minutes, or until a skewer comes out clean when inserted in the centre of the cake.
3. Leave the cake in the tin for 5 minutes before turning onto a wire rack to cool completely.
4. For the coconut icing, combine the icing sugar and coconut in a bowl, then add the lemon rind and enough lemon juice to make a stiff but spreadable icing. Spread the icing over the cold cake.