Preheat oven to 350 degrees F (175 degrees C). Grease a 9 x 5 inch loaf tin well.
Beat the egg whites until very stiff.
Cream butter or margarine and sugar until light and fluffy. Beat the egg yolks with the banana essence and the milk; stir into creamed mixture. Fold in bananas and walnuts. Sift the flour, and fold into the creamed mixture. Carefully fold in the egg whites. Pour batter into the prepared tin.
Bake for 40 to 50 minutes. Turn out onto a wire rack, and cool. Slice and serve.