Preheat the oven to 180°C, fan 160°C, gas 4. Lightly grease a 3lb loaf tin.
In a bowl, combine the flour, baking powder, cinnamon, bicarbonate of soda and salt. In another large bowl, whisk together the sugar and eggs, then add the oil. Stir in the carrots and apples.
Add the dry mixture to the wet, stirring until just blended. Pour into the prepared loaf tin and smooth the top. Bake for 1 hour, or until a skewer inserted into the cake comes out clean. Leave to cool in the tin for about 10 minutes, then tip on to a cooling rack to cool completely before icing.
For the frosting, beat the butter until smooth, using an electric mixer on a medium speed. Add the soft cheese and continue to beat. Reduce the speed of the mixer to low, add the icing sugar and vanilla extract, and continue to beat until the mixture is fluffy.
To assemble, cut the cake horizontally into three. Use the icing to sandwich the pieces together and smooth over the top. Decorate with sugar flowers.