Preheat oven to 220°C/Fan 200°C/425°F. Sprinkle a baking sheet 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 the pastry to a 1/4 inch thickness. Cut out 8 (5 inch) 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 centre 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.