Preheat the oven to 200 C, 180 Fan, Gas 6. Butter a 20 cm tart tin.
Put all the pastry ingredients into a food processor and pulse briefly so that the mixture just comes together. Press all but 3 tbsps evenly into the prepared tin and set aside.
Mix together all the filling ingredients except the berries. Spread three quarters of this mixture over the base of the tart. Toss the blackberries with the remaining dry mixture and tip on to the tart.
Crumble the reserve pastry on top and bake for about 40 minutes until crumbly and golden. Serve immediately.