Preheat the oven to 425°F (220°C) and dampen a baking sheet with water.
In a small saucepan over medium heat, melt butter. Stir in currants, demerara sugar, fruit peel, and mixed spice until sugar is dissolved and fruit is well coated. Remove from heat.
Roll the pastry on a lightly floured surface to 1/4 inch thickness. Cut out eight 5-inch circles using a saucer as a guide. Divide the fruit mixture evenly among the circles. Moisten the pastry edges with water, fold over the filling towards the center, and pinch to seal. Invert the filled cakes onto the floured surface and gently press to flatten into a wider circle, being careful not to tear the dough.
Glaze each cake with egg white and generously sprinkle with white sugar. Create three cuts across the top of each cake and place on the prepared baking sheet.
Bake until beautifully golden in the preheated oven for around 15 minutes.