Preheat the oven to 170C. Put two-thirds of the peeled banana chunks into a bowl and mash until smooth. Roughly mash the remainder and stir in gently.
Sift the flour, baking powder and salt into a bowl, and grease and lightly flour a baking tin about 21x9x7cm.
Put the sugar, eggs and melted butter in a large bowl and use an electric mixer to whisk them until pale and slightly increased in volume. Fold in the bananas and the dry ingredients until you can see no more flour, then fold in the walnuts.
Spoon into the tin and bake for about an hour until a skewer inserted into the middle comes out clean. Cool in the tin for 10 minutes before turning out on to a rack to cool completely.