Preheat the oven to 350˚F and line an 8x8 inch pan with parchment paper.
Prepare the topping by mixing the brown sugar, GF flour mix, chopped walnuts, cinnamon and salt. Slowly drizzle in the oil, stirring continuously, until all the oil has coated the dry mix. Set aside.
In a medium size bowl, whisk together the milk and vinegar. Allow to curdle and then whisk in the oil, yogurt and vanilla.
In a large bowl sift the flour, baking powder, baking soda and cinnamon. Stir in the sugar and salt. Make a well in the centre and add the wet mixture. Mix gently until almost mixed. Add the blackberries and mix again until evenly distributed. Do not over mix.
Scrape the cake batter into the lined pan and level out the top. Sprinkle the topping mixture evenly over the top. Bake in the centre of the oven for 40 to 50 minutes until an inserted toothpick comes out clean.
Allow to cool in the pan for about 30 minutes and then transfer to a wire rack to cool fully.