Preheat the oven to 160°C (325°F/Gas 3). Line a 30 x 23cm (12 x 9in) rectangular baking tin with parchment paper.
Place all the dry ingredients in a large bowl and make a well in the middle with the back of a spoon. Add the eggs, butter, milk and lemon zest and beat with an electric hand mixer until well combined, for about 2 minutes.
Pour the mixture into the lined tin, place on the middle rack in the oven and cook for 35 minutes until risen and golden brown on top. Turn out onto a wire rack and allow to cool completely before icing.
Whisk together the ingredients for the drizzle and spread over the top of the cooled lemon cake. Allow to set for about 1 hour before slicing into 30 pieces.