Preheat the oven to 180 deg C.
Lightly butter and line the loaf tin with parchment paper. Sift the flour, salt and baking powder into a large bowl. Add the sugar and butter and, using your fingertips, rub it in until the mixture resembles coarse breadcrumbs. Whisk the eggs, vanilla extract and orange zest in another bowl.
Add the bananas and mash very well with a potato masher. Add the chocolate chips. Make a well in the centre of the dry ingredients and pour in the banana mixture. Gently but thoroughly bring all the ingredients together with a wooden spoon, then pour into the prepared loaf tin.
Smooth the top and bake in the oven for 1-1 ¼ hours or until a skewer inserted into the middle comes out clean. Allow to cool for 5 minutes before removing the cake from the tin and leave to cool on a wire rack.