Preheat the oven to 180°C (160°C fan) and line a loaf tin with baking paper. In a large bowl, mash the bananas until smooth. Stir in the melted butter, brown sugar and beaten eggs until fully combined. Add the mead and mix again.
In a separate bowl, combine the self-raising flour, baking powder and salt. Gently fold the dry ingredients into the banana mixture until just incorporated. Crumble in the Christmas pudding, ensuring it is evenly distributed.
Pour the mixture into the prepared loaf tin and smooth the top. Bake for 50 to 55 minutes, or until a skewer inserted into the centre comes out clean. Leave the loaf to cool in the tin for ten minutes, then transfer it to a wire rack to cool completely.
To make the icing, sift the icing sugar into a small bowl and stir in the mead, a little at a time, until you have a thick consistency with a little movement. Drizzle the icing over the cooled loaf and allow it to set before slicing.