Line an 8-inch loaf pan with parchment paper and preheat oven to 350°F / 180°C. (or 160°C for fan oven).
Zest the lemons, then juice them into a separate bowl. Set aside the zest and juice.
Cream the softened butter and sugar together until light and fluffy.
Beat in the room temperature eggs, one at a time.
Sift in the dry ingredients, including the flour, baking powder, and salt. gently mix into the batter.
Add the lemon zest and mix it through the batter until evenly dispersed.
Pour the lemon batter into the prepared loaf pan and bake for 45-55 minutes or until a skewer inserted comes out clean.
Remove the cake from the oven and use a skewer to poke holes all over the cake, all the way to the bottom.
Sift the powdered sugar into a bowl then gradually add the squeezed lemon juice from earlier, a little at a time, mixing in between until you have added enough lemon juice to make a runny glaze.
While still warm and still in the pan, pour the glaze over the top of the cake, letting it all get soaked up by the cake. For best results, pour the glaze on about 10 minutes after removing the cake from the oven.
Let the cake cool completely before removing from the pan.
If you would like some additional, thicker glaze on top of the cake, you can repeat the steps to make the glaze but add less lemon juice. Pour this over the top of the cooled cake, once out of the pan.
Notes
Lemons - If possible, try to buy unwaxed lemons as you will be using the zest of the lemons. If you can't find unwaxed lemons, just soak the lemons in hot water for 5 minutes and then rub thoroughly with a dishtowel. Make sure the butter and eggs are at room temperature before beginning. I always recommend using a kitchen scale to weigh your ingredients rather than using cups. It's almost impossible to measure dry ingredients accurately with cups, and this can really mess up the end result of your bakes. All my recipes have measurements listed in both cups and grams so you can choose what works best for you. You can use the toggle at the top of the recipe card to switch between both.