Preheat the oven to 200°C/180°C Fan/Gas 6 and grease and line a 900g loaf tin with baking parchment.
Put the grated courgettes in a clean tea towel with a pinch of salt and give the towel a really hard squeeze a few times to get as much water as you can out of the courgettes.
Combine the flour, polenta, baking powder and 1 teaspoon of salt in a mixing bowl. Add the grated courgettes and mix well. In another mixing bowl combine the rest of the ingredients. Pour the wet ingredients into the bowl with the flour, polenta and courgettes. Gently fold the mixture together using a spatula. Do not overwork it or the loaf will be tough.
Transfer the batter to the loaf tin, spreading it out evenly using a spatula.Bake in the hot oven for 45–50 minutes. Check to see if the loaf is done by inserting a skewer into the centre of the loaf. If it comes out clean, it is done. If it’s still a little wet, put it back in the oven for another 5 minutes.
Turn the loaf out onto a wire rack and let cool before slicing.