Preheat the oven to 180°C, gas mark 4. Line a 900g (23cm x 13cm x 7cm) loaf tin with baking parchment. Sift the flour into a mixing bowl and stir in the caster sugar.
Whisk the eggs and buttermilk together in a small bowl. Pour in the butter and lemon zest and stir well. Fold this mixture into the flour together with the berries and combine. Tip into the loaf tin, sprinkle over the reserved sugar and cook for 45-50 minutes until the cake is well risen and golden. Check that a skewer inserted into the cake comes out clean. Leave in the tin for 10 minutes then remove and place on a rack to cool.
Make the icing by combining the icing sugar with enough of the lemon juice to make a smooth icing that coats the back of a spoon. Drizzle over the cooked cake. Store the loaf in an air-tight tin in a cool place for up to 3 days.