Preheat the oven to 160° fan and line a 12-hole muffin tin with cupcake cases.
Using a mixer, mix the flour, baking powder, sugar, butter, eggs, grapefruit zest until combined and then fold in the poppy seeds.
Divide the mixture between the 12 cupcake cases. Bake for about 20 minutes or until golden in colour. Insert a cake tester, if it comes out clean the cupcakes are ready. Remove from the oven, transfer them to a wire rack to cool completely.
While the cupcakes are baking, make the syrup. in a small pan combine the grapefruit juice and sugar. Bring to the boil then reduce the heat and simmer for 4 minutes until the syrup had thickened a bit. Remove from the heat and leave to cool a bit.
Using a skewer, poke holes in the warm cupcakes and paint over all the syrup using a pastry brush.
For the icing, mix the icing sugar and grapefruit juice together in a bow until smooth, a little more juice can be added if needed to reach your desired consistency. Spoon the icing over each cupcake and leave until the icing has firmed up.