Preheat oven to 350ᵒ F. Combine buttermilk and honey in a mixing bowl.
Sift the flour together with baking powder, baking soda, and salt. Stir about ⅔ of the flour mixture into the buttermilk. Slowly mix in the melted butter. Lightly stir in remaining flour, then the currants.
Turn onto a floured surface and knead dough gently for a few minutes. Divide into three equal sections. Flatten dough to form thick rounds about 4 to 5 inches in diameter. With a sharp knife, cut the rounds into 4 wedges each.
Place scones ½ inch apart on a buttered cookie sheet. Bake for 15 to 20 minutes or until golden. Remove from sheet and sprinkle with sugar, if desired. Serve warm with butter and preserves.