01 - Set oven temperature to 400°F (200°C, 180°C fan).
02 - In a large bowl, toss the apple slices with lemon juice, sugar, cinnamon, and flour. Gently fold in the blackberries.
03 - Line a 9-inch pie dish with half of the pastry, pressing into edges and trimming any excess.
04 - Spoon the fruit mixture evenly into the pastry-lined dish.
05 - Roll out remaining pastry and place over the filling. Trim and crimp edges to seal. Cut small slits in top for steam to escape.
06 - Brush the pastry surface with beaten egg and sprinkle with demerara sugar.
07 - Bake in preheated oven for 45 to 50 minutes, until crust is golden and filling bubbles.
08 - Let the pie cool for 10 to 15 minutes before serving warm.