Place the tea bags in a heatproof measuring jug and pour in the boiling water. Stir, then leave to infuse for 3 to 4 minutes. Put the lime juice, zest and sultanas in a bowl. Remove the tea bags, and pour the tea over the fruit. Cover and set aside to soak for at least 5 hours or overnight.
Preheat the oven to 160 C / Gas 3. Grease and line a 900g loaf tin. Sift the flours and baking powder into a bowl, tipping in any bran left in the sieve. Stir in the sugar.
Pour in the soaked dried fruit, scraping in all the liquid from the bowl, and add the beaten egg. Lightly mix the egg and fruit together, then stir in the dry ingredients until thoroughly combined. The mixture should be soft enough to drop easily off the spoon. Add 2 to 3 teaspoons more hot water if needed.
Spoon the mixture into the prepared tin and spread it out evenly.
Bake in the preheated oven until the loaf is well risen and firm, cracked along the middle and browned on top, about 1 1/4 hours. Cover loosely with foil for the last 20 minutes of baking if it is becoming too brown.
Leave to cool in the tin for about 5 minutes, then turn out onto a wire rack to cool completely.
This bara brith tastes particularly good if it is left for 1 to 2 days before eating. It can be kept, in a polythene bag in a cool place, for about 5 days.