Preheat oven to 180C/360F fan forced. Spray a loaf tin with oil and line with baking paper so that it hangs over the long sides of the tin.
Beat the egg whites and sugar together in a medium bowl for one minute.
In a bowl or jug, mix the bicarb soda into the apple sauce (it will froth).
Add the cinnamon, allspice and apple mixture to bowl then stir in the mashed banana.
Gently fold in the flour and walnuts in one go.
Pour the mixture into the tin and bake for approximately 30-35 minutes or until it springs back in the middle.
Leave the cooked bread in the tin for about 5 minutes before transferring to a wire rack to cool.