Place the butter and sugar in an electric mixer and mix on a medium speed until fluffy. In a separate jug combine the eggs and milk. Now add the milk mixture to the sugar mixture a little at a time, continuing to mix on a slow speed. Once all the milk mixture and sugar mixture are combined, add the rice flour, potato starch, baking powder, lemon zest and juice. Work in by hand using a spatula.
When all ingredients are mixed together pour the batter into your loaf tin and put in the oven for about 50 minutes. While the cake is cooling on a wire rack combine the icing sugar, lemon juice and vodka in a small mixing bowl. The consistency should be very runny, you want a liquid to drizzle over the cake, not icing to spread on a cake.
Once the cake has cooled use a skewer to push several holes in the top if the cake. The idea is to have small openings for the drizzle to enter, you could make them with a small, sharp knife if you prefer. Now slowly pour the drizzle over the cake a little at a time. You want the cake to absorb it rather than have it all running down the sides.
Wait about half an hour for the drizzle to set then enjoy your low FODMAP lemon drizzle cake!