Preheat the oven to 180C/350F/gas mark 4. Grease an approx 11.5 x 21.5 cm / 4.5 x 8.5 in loaf tin and line with a strip of baking parchment. Make sure that you leave some overhanging on either side so that you can lift the cake out easily.
Whisk together the light brown soft sugar, caster sugar, oil, milk, vinegar, vanilla and lemon or orange zest in a large bowl.
In a separate bowl, sift together the plain flour, wholemeal flour, baking powder, bicarbonate of soda, cinnamon, ginger, nutmeg and salt.
Tip the dry ingredients into the wet and whisk gently until no lumps of flour remain. Be careful not to over-beat the batter however as that can make the cake tough.
Add the grated carrots and fold through until well combined.
Pour the batter into the prepared tin, spread it level and bake for about an hour until a skewer inserted into the centre comes out clean.
Let the cake cool in the tin for about 20 minutes then carefully lift it out using the strip of baking parchment and place it on a wire rack to cool completely.
To make the glaze, place the sifted icing sugar in a bowl and add the yoghurt (if using). Gradually stir in the lemon juice until it forms a thick but pourable glaze.
Pour the glaze over the top of the cake and serve. Store any leftovers in an airtight container.
For the best results make sure that you follow the recipe closely. As always, I highly recommend using the gram measurements (with a digital scale), rather than the cup conversions. Cup measurements are simply not accurate enough for baking and I cannot guarantee the best results if you use them.