Place the sultanas, raisins, cranberries, currants, apricots, apple, and carrot in a bowl. Add the orange and lemon juice and pour in the measured brandy, rum, or sherry, along with the cider. Stir the ingredients together and refrigerate overnight.
In a large bowl, place the measured butter, sugar, and grated orange and lemon zests. Cream these together until they become light and fluffy, using either a wooden spoon or a hand-held whisk.
Gradually introduce the eggs into the creamed mixture. If the mixture begins to curdle, add a small portion of the measured flour.
Sift the mixed spice into the flour. Fold into the creamed mixture along with breadcrumbs and nuts. Incorporate the soaked dried fruits and their soaking liquid, stirring well.
Take a 1.4-litre/2½ pint pudding basin and generously coat it with butter. Insert a small disc of foil or baking parchment into the basin's base.
Spoon the prepared mixture into the pudding basin and press it down using the back of a spoon. Cover the pudding with pleated layers of baking parchment and foil, securing them with string. Trim any excess paper and foil with scissors.
To steam, place the pudding in the top section of a steamer filled with simmering water. Cover it with a lid and steam for eight hours, replenishing the water as needed.
To boil, create a trivet by putting a metal jam jar lid or metal pan lid in the base of a large pan. Insert a long, doubled strip of foil between the trivet and the pudding basin to make it easier to lift the hot pudding basin out of the water once it's cooked.
Gently lower the pudding onto the trivet and pour enough boiling water into the pan to reach halfway up the side of the bowl. Add a quarter of a lemon to prevent staining. Cover with a lid, bring the water to a boil, then maintain a rolling simmer for about seven hours until the pudding turns deep brown. Remember to top up with boiling water as necessary. Set a timer to check the water level every 30 minutes.
Once the pudding is cooked through, remove it from the pan and allow it to cool completely. Discard the paper and foil, replacing them with fresh ones. Store the pudding in a cool, dry place.
On Christmas Day, steam or boil the pudding for about two hours to reheat. Invert the pudding onto a serving plate. You can flame the pudding by warming a tablespoon of brandy or rum in a small pan, pouring it over the hot pudding, and carefully igniting it.
Serve the pudding with an accompaniment of your choice.