Line and grease a 9 inch loaf tin (2lb loaf tin) and pre-heat oven to 180°C/ 160°C fan assisted / gas mark 4 / 350°F.
Place the sugar and lime zest into a large mixing bowl. Rub the lime zest into the sugar using your fingertips until fragrant.
Add the butter into the lime sugar and mix, using either a stand mixer or an electric mixer, for 1-2 minutes until light and creamy. Scrape down the sides of the bowl every so often.
Add in the eggs one at a time, mixing well between each addition.
Whisk together the gluten-free flour, desiccated coconut, baking powder and salt in a separate bowl then add to the rest of the cake mixture. Mix well until fully combined.
Pour the cake mixture into the prepared loaf tin and bake for 60 minutes or until an inserted cocktail stick comes out clean.
Remove from the oven and leave to cool slightly in the tin whilst you prepare the drizzle.
Mix the lime juice, desiccated coconut and granulated sugar together.
Turn the cake out of the tin and turn the right way up. Poke holes all over the surface using a cocktail stick, then pour the drizzle over.
Cool completely before serving, slicing a fresh lime to decorate the top of the cake.