Preheat oven to 200C/392F.
Peel, quarter, core, and thinly slice the apples and toss them in a bowl with 2 tablespoons flour and half the sugar, then gently mix in the blackberries.
Arrange the fruit in a shallow 2 liter or 30cm oval gratin or ovenproof dish
Dice the chilled butter. Combine the remaining flour, oats, and remaining sugar in a bowl and rub in butter until you have large crumbs.
Scatter the crumble over the fruit and bake for 35 minutes, until the top is golden and crisp and juices are bubbling up at the sides. Leave to cool 20-30 minutes.