Line a large loaf tin with baking paper and preheat your oven to 150 degrees.
In the bowl of an electric mixer, add the butter, vanilla extract, caster sugar, eggs, flour, baking powder, bicarbonate of soda, milk and lemon rind.
Mix on a low speed until all the ingredients have combined and then increase to a medium/high speed and mix until the mixture is smooth.
Pour the mixture into your prepared cake tin and place in the oven to bake for 45 minutes or until the cake is cooked through when tested with a skewer.
Carefully remove the cake from the oven and let it cool in the tin for 10 minutes before carefully transferring to a wire rack to cool completely.
Once cool, prepare the lemon icing by sifting 1 1/4 cups of icing sugar into a bowl and adding 2 tablespoons of lemon juice. Mix the ingredient together until they are smooth.
Use a spatula or a butter knife to then spread the icing over the cake.