Grease and line a 30 × 20cm baking tin with greaseproof paper.
Ideally using an electric mixer (but a wooden spoon will do, if need be), mix the butter and sugar until creamed.
Add the eggs, one at a time, and mix to combine. Stir in the vanilla extract and orange zest, then fold in the flour and baking powder. If the cake batter is too thick, add the milk one tablespoon at a time and mix.
Transfer the cake batter to the baking tray and bake for 30-35 minutes, until a cocktail stick inserted into the centre comes out clean. Leave to cool in the tin.
While cooling, heat the mulberries or raspberries with 2-3 tablespoons of water until soft. This will take around five minutes. Once soft, pass through a sieve into a clean mixing bowl, using the back of a spoon to squeeze out as much juice as possible. You should have around 5 tablespoons of liquid. Add a little cold water if necessary.
Add the icing sugar, one tablespoon at a time, and whisk. Start with 300 grams, but if the icing is too thin, add another 50 grams or so until the consistency is correct. It should resemble smooth wallpaper paste.
Gently remove the cooled cake from the baking tray and spoon the icing over the top. Smooth using a palette knife and leave to set. Once set, cut the cake into squares and serve.