Preheat the oven to 350 °F and grease the loaf pan.
In a large bowl, blend the room temperature butter until light and fluffy. Add the sugar and mix until combined.
Add the eggs to the mixture one at a time, mixing in between. Add the milk and vanilla.
In a separate, medium bowl, whisk together the flour, salt, and baking powder. Add the dry ingredients to the wet ingredients. Mix until just combined.
Add the lemon zest, lemon juice, and elderflower syrup. Mix until just combined. Batter will be thick.
Pour the batter into the greased loaf pan. Bake for 45-55 minutes until a toothpick comes out clean in the middle.
Combine the powdered sugar, lemon juice, and elderflower syrup in a small bowl.
Once cake is cool to the touch, pour the glaze over the cake. Slice and enjoy!