Heat oven to 180ºC (160ºC fan). Grease and line a 1lb loaf tin with greaseproof paper.
Cream the butter and sugar together until smooth (by hand or electric mixer).
Add the eggs one at a time and stir in well.
Sift in half the flour with the bicarbonate of soda and salt, and mix.
Add in the milk and stir in followed by the remaining flour, chocolate chips and vanilla.
Cut up the bananas in to small chunks (or mash them up) and then fold them in to the mixture.
Fill the loaf tin with the mixture and bake for around one hour until golden brown and until a skewer inserted in the middle comes out clean. Cover the top with foil if it starts to brown too quickly.
Allow to cool in the tin for at least 10 minutes before turning out. To serve, cut into thick slices and serve warm or at room temperature.