Preheat the oven to 350F(176C). Grease and flour a 7 inch loaf pan.
In a large bowl sift flour, baking powder, baking soda and salt. Set aside.
In another bowl, beat softened butter and cream cheese until smooth and well combined.
Gradually add sugar to the butter-cream cheese mixture. Beat for approximately 5 minutes until the mixture becomes light and fluffy.
Add vanilla extract and lemon zest to the mixture. Beat until well incorporated.
Add eggs one at a time, beating well after each addition. This ensures the eggs are fully incorporated into the batter.
Gradually add the sifted dry ingredients to the wet mixture in three batches. Gently fold the dry ingredients into the wet mixture using a spatula. Mix until just combined; avoid overmixing to maintain the cake's texture.
Pour the batter into the prepared loaf pan. Bake for 45-50 minutes or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for a few minutes. Then, transfer it to a wire rack to cool completely before slicing.