Preheat your oven to 180°C / 160°C (fan) / Gas Mark 4 / 350°F.
Grease and line two 8-inch round cake tins.
In a large mixing bowl, cream together the butter, sugar, and vegetable oil until pale and fluffy.
In a separate bowl, whisk the eggs, milk, and vanilla extract until combined.
Gradually add half the wet mixture to the creamed butter, mixing until smooth.
Sift in half the flour and gently fold it into the batter. Repeat with the remaining wet and dry ingredients.
Finally, fold in the baking powder until just combined.
Divide the batter evenly between the prepared tins and bake for 25–30 minutes, or until a skewer inserted into the center comes out clean.
Let the cakes cool in their tins for 20 minutes before transferring them to a wire rack.