Preheat your oven to 180 C / Gas 4. Line a muffin tin with paper cases.
Beat the butter and sugar together till pale and creamy. Lightly whisk the eggs together with the vanilla, then add gradually to the butter mixture, beating well.
Combine the flour, bicarb and baking powder in a separate bowl. Add to the butter mixture and fold together gently, adding milk only as needed to achieve a smooth mixture that drops easily from your spoon. Spoon the cupcake mixture into the prepared cases, about half full.
Bake for 10 to 15 minutes in the preheated oven, or till golden and risen. Remove from oven and cool in the tin slightly before removing from the tin to cool completely.