Begin by preparing your baking tins and preheating the oven to 350°F (175C/155C Fan).
In a large mixing bowl, use a handheld electric beater to cream together the sugar and butter until light and fluffy (about 2 minutes). Then add the eggs one at a time beating after each addition.
Add the yogurt, vanilla extract, lemon zest and juice to the mixture and beat to combine.
Sift together the flour, baking soda, baking powder, salt and almond flour into the bowl and stir with a spatula until just combined.
In a small bowl, toss 8 oz blackberries with a spoon of flour to coat. Then add half of these to the batter and fold to incorporate.
Pour the batter into two 7.5" round cake tins (see note) and smooth evenly. Scatter the remaining blackberries over top of the layers - this will help them to distribute in the batter.
Bake in a preheated oven for about 50 minutes, checking for a toothpick inserted in the centre to come out clean.
Once baked, remove from the oven and cool for 5 minutes in the pans before turning out onto wire racks to finish cooling.