Preheat oven to 170ºC / 340ºF. Grease and flour a loaf or cake pan. I used 3 small ones.
Cream together sugar, butter and lemon zest. Add eggs, one at a time and beat until smooth.
In another bowl, sift together flour and baking powder. Fold into the wet ingredients and beat on low speed until fully incorporated. Add milk, mix and pour into the prepared pan. Bake for 45 minutes or until a toothpick inserted in the center comes out clean. Baking time will vary depending on the size of the pan you use. Let cool.
For the glaze: In a small bowl, mix the powdered sugar and lemon juice. If it is too thick, add a few more drops of lemon juice; if it is too thin, add a little more sugar. Spread the glaze over the cooled loaf and allow to set.