In a large bowl, combine 1 cup sugar, cornstarch, tapioca, blackberries, lemon peel, and lemon juice. Mix gently to coat. Pour into a shallow 3- to 4-quart baking dish.
In another bowl, mix flour, baking powder, salt, and remaining 1/4 cup sugar. With your fingers or a pastry blender, rub or cut butter into flour mixture until coarse crumbs form. Add cream and stir just until mixture forms a soft, crumbly dough.
Pat 1/4-cup portions of dough into flat disks 1/2 inch thick and arrange evenly over fruit.
Bake in a 350º oven until topping is golden brown and fruit is bubbling, 45 to 55 minutes. Serve warm or at room temperature.