Place an oven rack in the centre of the oven. Preheat the oven to 180c. Butter and flour a 9- by 5- by 3-inch loaf pan. Set aside.
In a medium bowl, whisk together the flour, baking soda, salt, baking powder, cinnamon and nutmeg. In a large bowl, beat the sugar, oil, eggs and vanilla until blended. Stir in the bananas, mango and blueberries. Add the dry ingredients and stir just until blended.
Pour the batter into the prepared loaf pan. Bake until a cake tester inserted in the centre of the loaf comes out clean, about 1 hour. Cool for 15 minutes. Remove the loaf from the pan and cool completely on a wire rack, about 2 hours.