Preheat the oven to 180 C / Gas 4. Grease a loose-bottomed 23cm (9 in) round cake tin, and line the bottom with baking parchment.
Combine the butter, sugar, flour, baking powder, almonds, eggs and milk in a bowl. Beat well for about 2 minutes, or till smooth and well blended. Spoon mixture into cake tin, then arrange the halved apricots on top, cut-side down, pressing down lightly.
Bake for 50 minutes or until golden brown and firm to the touch, covering with foil after 30 minutes if the cake begins to brown too much. Cool for 10 minutes in the tin, then run a knife along the sides and remove the ring of the tin and allow the cake to cool completely.