Preheat the oven to 180 C / Gas 4. Line a cupcake pan with paper liners; set aside.
In a medium bowl, sift together flour, baking powder, and salt. In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar until light and fluffy. Add eggs, one at a time; scrape down bowl, and beat in vanilla.
Add flour mixture and milk alternately, beginning and ending with flour mixture. Divide batter evenly among liners, about three-quarters full each.
Bake until golden and tops spring back to touch, about 20 minutes, rotating pan once if needed. Transfer pans to wire rack; cool completely.