Pre-heat the oven to 160°C (320°F).
Cream the butter and sugar until smooth. Beat in the egg.
Sift the flour and baking powder, and fold into the batter. Add the lime juice, followed by the milk, stirring until well combined.
Fill eight cupcake cases about half way, then place in the middle of the oven, and bake for around 15-17 minutes. They will be ready when an inserted skewer comes out clean.
Leave on a wire rack to cool.