Preheat the oven to 180C/160C Fan/Gas 4. Grease a 900g/2lb loaf tin (20x12.5cm/8x5in).
Sift the flour, bicarbonate of soda and salt into a large mixing bowl.
In a separate bowl, cream the butter and sugar together until light and fluffy.
Add the eggs, mashed bananas, buttermilk and vanilla extract to the butter and sugar mixture and stir to combine. Fold in the flour mixture.
Pour into the prepared tin and bake for about an hour (check after 45 minutes), or until well-risen and golden-brown.
Remove from the oven and cool in the tin for a few minutes, then turn out onto a wire rack to cool completely before serving.
