In a medium saucepan, combine 1/3 cup sugar and 2 tablespoons butter. cook over medium heat until melted.
Add currants, candied peel, nutmeg and allspice. Continue to cook until heated through.
Remove from heat and allow to cool.
Preheat oven to 425 degrees F (220 degrees C).
On a lightly floured surface, roll out pastry to a thickness of 1/8 inch.
Cut into 4 inch rounds.
Place a small spoonful of filling onto center of each pastry circle, draw the edges together over the fruit and pinch to seal. Turn over, then press gently with a rolling pin to flatten the cakes.
Make a small hole or 2 small slash marks in the center of each pastry.
Brush with beaten egg white, and sprinkle with sugar. Arrange on cookie sheet.
Bake in preheated oven for 15 minutes, or until lightly browned around edges.
