Preheat the oven to 325°F/165°C. Grease and flour a 2lb loaf tin or line it with baking parchment.
In a large bowl, cream together the butter and sugar until pale and creamy. Add in the eggs one at a time, mixing well after each addition. Mix in the lemon zest and poppy seeds.
Add the flour and baking powder, mixing until well combined. Pour the batter into the prepared loaf tin and bake for 45-60 minutes, until a skewer comes out clean and the top is golden. Leave to cool inside the loaf tin.
While the loaf is cooling, mix together the lemon juice and sugar to make the drizzle. Prick the warm loaf all over with a skewer and pour the drizzle over it. Leave to cool completely in the tin before serving.