Preheat the oven to 180°C.
Butter a 26cm x 9cm x 8cm loaf tin and line it with greaseproof paper.
Whisk eggs, sugar, cream, lemon zest, rum, salt, and butter in a large bowl.
Sift flour and baking powder into the mixture and whisk until smooth.
Pour batter into the tin and bake for 50-60 minutes, turning halfway.
Remove cake from tin and cool on a rack for 10 minutes while keeping the oven on.
Brush the cake with warmed apricot glaze and rest for five minutes.
Combine lemon juice, zest, and icing sugar for the lemon glaze.
Heat the lemon mixture until the sugar dissolves into a syrup.
Brush the lemon syrup over the cake and let it set.
Place cake in the turned-off oven for 3-5 minutes to dry the glaze.
Remove from the oven and cool to room temperature before serving.