Place raisins, currants, prunes, and mixed peel in a food processor; process until finely chopped. Transfer to a large jar.
Pour cherry brandy, 1/2 cup brown sugar, dark rum, and mixed spice into the jar; mix well and seal. Refrigerate, stirring occasionally, until flavors blend, 2 weeks to 3 months.
Preheat oven to 325 degrees F (165 degrees C). Grease and line two 9-inch cake pans with parchment paper.
Combine butter and 1 3/4 cup brown sugar in a bowl; beat with an electric mixer until smooth and creamy. Beat in eggs until smooth. Beat in raisin mixture until evenly incorporated. Fold in flour and vanilla extract gradually until batter is smooth and falls off the back of a lifted spoon.
Divide batter between the prepared cake pans. Cover cake pans loosely with aluminum foil.
Bake in the preheated oven until cakes are firm and spring back when lightly pressed, about 2 1/2 hours.
Cool cakes in the pans, 8 hours to overnight. Wrap in aluminum foil to keep moist.