For the cake:
Preheat oven to 180 degrees (160 degrees fan forced) and grease and line the base of a 22cm x 10cm log tin.
Combine the softened butter, sugar and orange rind in a bowl and using an electric mixer, beat until it's pale and fluffy.
Beat in eggs one at a time, making sure they are completely combined.
Sift the flour over the top of the cake, and while on a low speed, slowly add the orange juice and milk and continue to beat until the mixture has combined.
Pour mixture into the prepared tin and lightly smooth over the top.
Bake in oven for approximately 45 minutes, until the cake is firm to touch on top and cooked through.
After removing from oven, cool cake in tin for 15 minutes before turning onto a wire rack to cool completely.
Add the butter, rind, and icing sugar into a bowl.
Add the orange juice and using a metal spoon mix until combined and you have a smooth consistency.
If the icing is a little hard to spread, just add a few extra drops of orange juice.