Preheat the oven to 170°C. Grease and line a cake tin.
In a saucepan, combine the butter, brown sugar, golden syrup, black treacle, dark rum and milk. Heat gently until the butter has melted and the mixture is smooth. Remove from the heat, stir in the freshly grated ginger and allow to cool.
In a large bowl, whisk together the self-raising flour, bicarbonate of soda, cinnamon, ground ginger, ground lemon myrtle, chopped crystallised ginger and salt.
Pour the cooled syrup mixture into the dry ingredients. Add the egg and whisk until smooth and glossy.
Pour into the prepared tin and bake for 40 to 50 minutes, or until a skewer inserted into the centre comes out with a few moist crumbs attached. The cake should remain slightly sticky in the centre.
Cool in the tin for 10 minutes before transferring to a wire rack.
Mix the icing sugar with the lime zest. Gradually whisk in enough lime juice to create a thick, pourable glaze. Drizzle over the cooled cake and allow to set before serving
