Preheat oven to 180C/350F. Grease a 20cm x 30cm (8-inch x 12-inch) lamington pan; line base with baking paper, extending paper 5cm (2 inches) over long sides.
Beat butter, sugar and egg in a small bowl with an electric mixer until light and fluffy. Transfer to a medium bowl; stir in sifted flours and custard powder. Spread dough into pan; spread with jam.
Make coconut topping by combining all ingredients into a small bowl; sprinkle topping over jam.
Bake for about 40 minutes, then cool in the pan.