Place the flours in a large bowl, add the butter and rub in with the fingertips until the mixture resembles fine breadcrumbs. Stir in the caster sugar and salt. Mix in 3½–4½ tablespoons cold water, adding enough water to form a dough, and knead lightly until smooth. Divide into 2 balls, one slightly larger than the other. Wrap each in clingfilm and chill for 30 minutes.
Put the apples, lemon juice, almond essence and brown sugar in a bowl and toss to coat. Mix in the blackberries and set aside.
Roll out the larger ball of pastry on a lightly floured surface to fit a 23 cm (9 inch) nonstick pie tin. Press the pastry into the tin to come up the sides, moistening the edges with a little cold water. Roll out the smaller ball to fit as a lid. Spoon the fruit evenly over the pastry shell, then scatter over the almonds, if using. Top with the pastry lid, pressing down the dampened edges to seal. Trim away the excess pastry with a sharp knife.
Cut 3 small incisions in the top of the pie and place in a preheated oven, 180°C (350 °F), Gas Mark 4, for 35–40 minutes or until crisp and golden. Leave to rest for 5–10 minutes, then serve in slices with half-fat crème fraîche.