Preheat oven to 425° F. In a large bowl stir together the flour, sugar, baking powder, baking soda, and salt until thoroughly blended. Using a pastry blender or two knives, cut the butter into the flour mixture until it resembles coarse cornmeal. Stir in the currants and the orange peel.
Make a well in the center of the butter-flour mixture and add the buttermilk all at once. Stir the mixture with a fork until the dough pulls away from the sides of the bowl.
With your hands, gather the dough into a ball; turn out onto a lightly floured board. Divide the dough into 2 parts. Pat each into a 7-inch circle 1 inch thick. Using a sharp knife, score each into 8 pie-shaped wedges.
Place the scones 1-½ inches apart on a lightly greased baking sheet. Brush the tops with the cream or milk and sprinkle with the sugar-cinnamon mixture. Bake 12 minutes or until the tops are lightly browned.