Beat the butter, sugar and lime zest together in an electric mixer or by hand in a medium sized mixing bowl with a wooden spoon.
Gradually add the eggs, beating well between each addition until fully incorporated.
Now, gently fold in the flour and then the blueberries. Add a drop of milk to let the mixture down a bit.
Place you paper muffin cases in a bun tray and then spoon the cake mixture evenly between them.
Place into your oven for about 10-12 minutes or until risen, golden brown and firm to the touch. As you gently touch the cake it should spring back. If it's still a bit wobbly in the middle, pop back into the oven for a few more minutes.
Take out of the trays and place on a cooling rack. When cool you are ready to ice.
For the Icing:
Using an electric mixer (you can do by hand, but the mixer makes this frosting extra light) beat the butter and cream cheese together until thick and creamy. Gradually beat in the icing sugar and then the lemon juice and purple food colour.
Leave in the fridge to set for 20 minutes then pipe.