Preheat the oven to 160 degrees C. Grease a 30cm round cake tin.
Beat the butter, sugar and vanilla together until pale and light. Beat in the eggs, one at a time, then fold in the lemon zest and lemon juice. Fold in the polenta, baking powder and salt and mix well. Spoon the cake mixture into the prepared cake tin.
Bake in the preheated oven for 45 to 50 minutes or until a skewer inserted into the centre comes out clean.
Allow to cool fully on a cooling rack before serving.