Heat oven to 180C/160C fan/gas 4. Butter and line the base of 2 x 20cm cake tins with baking parchment. Beat the butter and light brown sugar together until pale and fluffy. Add the eggs gradually, beating well between each addition. Fold in the flour, baking powder and cocoa powder. If the mixture is very stiff, stir in the milk.
Spoon into the cake tins and bake for 20-25 mins or until a skewer inserted into the centre comes out clean. Turn the cakes out onto a wire rack and peel off the parchment. Gently heat the lime juice and caster sugar together, stirring to help the sugar dissolve. While the cakes and the syrup are still warm, pierce the cakes all over using a skewer and spoon over the syrup. Leave to cool completely.