Preheat the oven to 325°F (160°C), Gas mark 3 and line a 9in x 12in (23cm x 30cm) baking tin with parchment paper.
Sift the flour into a large bowl with the baking powder and sugar. Make a well in the center and add the butter, eggs, lemon rind and milk. Beat with a hand-held electric mixer for a couple of minutes until well combined.
Using a spatula, transfer the mixture to the prepared tin and spread out evenly. Place in the oven for 30-35 minutes until well risen and golden brown. Leave in the tin for a few minutes then transfer to a wire rack to cool completely.
To make the icing, sift the icing sugar into a bowl and add the lemon rind and juice, then beat until smooth. Spread over the top of the cooled lemon cake. Leave to set at room temperature for 1 hour and then cut into squares.
To serve, arrange squares of the lemon drizzle cake on a large plate and place on the table so that guests can help themselves.