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, poppy seeds, 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 cream cheese icing by placing 250g of softened cream cheese and 100g of softened butter into an electric mixer and beating for 3 - 4 minutes until well combined. Add 1 ¼ cups of icing sugar and 1 teaspoon of vanilla extract and mix well to combine.
Use a spatula or a butter knife to then spread the icing over the cake.