Heat oven to 160C/140C fan/gas 3. Grease and line a 900g loaf tin with baking parchment. In a saucepan, heat the apricots with the orange zest and all but 1 tbsp of the juice. Simmer gently for 5 mins until the apricots have absorbed all the juice. Set aside to cool.
Beat the butter and sugar in a bowl until light and fluffy. Gradually beat in the eggs, then fold in the flour. Stir in the cooled apricots. If the mixture is dry at this stage, add a drop of milk.
Scrape the batter into the tin and smooth the top with a spatula. Bake for 50 mins-1 hr until a skewer inserted into the middle comes out clean. Cool in the tin for 10 mins before removing, then leave on a wire rack to cool completely.
Gradually add the reserved orange juice to the icing sugar, stirring until smooth and slightly runny. Drizzle the icing in a zigzag pattern over the top of the cake and leave to set.