Heat the oven: Heat the oven to 190 degrees C (170 degrees C fan). Lightly butter a medium baking dish, about 20 by 28 cm.
Prepare the berries: Put the berries in the dish, hulling and halving any large strawberries. Sprinkle over the sugar, cornflour, lemon juice, and vanilla, and toss gently until coated. The cornflour helps thicken the filling so it is jammy rather than watery. Taste a berry: if they are very tart, add another spoon of sugar.
Make the topping: Put the flour, oats, sugar, and salt in a bowl, add the cold butter cubes, and rub them in with your fingertips until you have rough breadcrumbs with some larger pea-sized clumps. Those clumps go crisp in the oven. Do not melt the butter, and do not overmix into a smooth dough.
Assemble and bake: Scatter the topping evenly over the berries, keeping it loose rather than pressing it down. Bake for 35 to 40 minutes, until the topping is deep golden and the berry juices are bubbling at the edges. If the top browns too fast, cover loosely with foil for the last 10 minutes.
Rest and serve: Rest the crumble for 10 minutes so the filling thickens slightly and stops being runny. Spoon into bowls and pour custard, cream, or ice cream over the top.