Preheat the oven 350F (180C). Line an 8-inch by 2-inch loaf pan with a piece of parchment paper long enough to hang over the sides (this helps to easily lift the cooled cake from the pan).
Set about making the topping first. Add the flour, sugar, salt, and cinnamon to a small bowl. Whisk to blend. Add the melted butter, and stir until it forms a wet, sandy-looking mixture.
To make the cake batter, add the flour, sugar, baking powder, baking soda, and salt to a deep bowl. Whisk to blend. Add the egg, buttermilk, and melted butter. Use a fork to stir the batter just until it’s combined, and there are no visible signs of flour (it’s okay to see a few little lumps). Gently fold in the blackberries.
Spoon the batter into the prepared pan. Evenly scatter the crumb topping over the batter.
Bake 40 to 45 minutes, until the cake is golden, and a metal skewer inserted in the center comes out clean.