Preheat oven to 180°C. Butter and line a loaf tin.
Cream the butter and caster sugar. Add eggs and lemon zest, beating well. Gently fold in flour and salt, then milk. Spoon into prepared loaf tin and bake for 45 minutes.
While cake is cooking, place lemon juice and icing sugar in a small saucepan and heat gently until the sugar dissolves.
When the cake is golden and risen in the middle, remove it from the oven and puncture the top all over with a skewer or knife. Pour the syrup over the cake, making sure that the middle as well as the sides are soaked by it.
Wait until the cake is completely cold before removing it from the tin. It will be saturated with syrup, and will be fragile.