Preheat oven to 220 degrees C. Sprinkle a baking tray with water.
In a small saucepan over medium heat, melt butter. Stir in currants, mixed peel, demerara sugar and mixed spice. Stir until sugar is dissolved and fruit is well coated. Remove from heat.
On a lightly floured surface, roll out pastry to a 5mm thickness. Cut out 8 circles, using a saucer as a guide. Divide the fruit mixture evenly between the circles. Moisten the edges of the pastry, pull the edges to the center and pinch to seal. Invert filled cakes on the floured surface and roll out gently to make a wider, flatter circle, but do not break the dough.
Brush each cake with egg white and sprinkle generously with white sugar. Make three parallel cuts across the top of each cake, then place them on the prepared baking sheet.