Preheat the oven to 350°F. Grease a 2 lb loaf pan, line the base and sides with waxed paper and grease the paper.
Place the butter together with the sifted flour and baking powder into a mixing bowl, then add the sugar, eggs and lemon zest. Beat for 1 - 2 minutes until smooth and glossy, and then stir in the apricots, almonds and pistachio nuts.
Spoon the mixture into the prepared pan and smooth the surface. Bake in the center of the oven for about 1-1/4 hours, or until a skewer inserted into the center of the cake comes out clean. Check the cake after about 45 minutes and cover with a piece of foil when the top is nicely brown. Leave the cake to cool in the pan.