Preheat Oven and Prepare Tin: Preheat your oven to 180°C (350°F) and grease your cake tin, lining it with baking parchment.
Mix Dry Ingredients: Combine the flour, baking powder, and a pinch of salt in a bowl by sifting them together.
Cream Butter and Sugar: In a separate bowl, cream the softened butter and sugar until pale and fluffy.
Add Eggs: Introduce the eggs into the mixture one at a time, blending thoroughly after each addition to ensure they are well incorporated.
Incorporate Lemon and Courgette: Stir in the lemon zest, lemon juice, and grated courgette.
Combine Mixtures: Fold the dry ingredients into the wet mixture using a rubber spatula until the batter is smooth.
Prepare to Bake: Transfer the cake batter into the greased baking tin, leveling the surface smoothly. Bake in the oven for 35-40 minutes, or until a skewer comes out clean when inserted into the middle of the cake.
Cool and Ice: Allow the cake to cool in the tin for 10 minutes, then turn out onto a wire rack to cool completely. Mix the icing sugar with lemon juice to create a drizzle and pour over the cooled cake.