Preheat the oven to 325ºF. Prep an 8-inch cake pan by greasing and flouring it, and lining the bottom with a round of parchment.
Mix the raisins and mixed peel with the ¼ cup of rum and heat it in a saucepan or microwave the mixture to plum the fruit. Let soak, and set aside to cool.
In the bowl of an electric mixer fitted with the paddle attachment, cream together the butter and the sugar. Add the eggs one at a time, beating each one in before adding the next, and scraping down the sides of the bowl as needed. Add the vanilla.
In a separate bowl, whisk together the flour, nutmeg, salt, and baking powder.
Strain the plumped fruit, saving the rum. Mix the plumped fruit with 2 tablespoons of flour to coat them.
Add half of the dry mixture to the mixer bowl and beat it in, followed by the saved rum, and then add the last of the flour. Fold in the plumped fruit with a spatula.
Spread the cake batter in the prepared pan and bake it for about 30 minutes or until a cake tester inserted into the centre comes out clean. Let cool 10 minutes before unmolding the cake onto a wire rack to cool completely.
To make the frosting
Cream together the butter with the icing sugar, then add the rum and the vanilla.
Spread the frosting thickly over the cake before serving.