Heat the oven to 180C/fan 160C/gas 4 and oil and line a deep 20cm springform cake tin. Whisk together the sugar and olive oil in a bowl. Add the eggs, one at a time, with 1 tbsp of flour until completely incorporated. Whisk in the remaining flour and 1/2 tsp salt. Whisk in 125ml of the yogurt, the vanilla and lemon zest, then pour into the tin. Push the blackberries into the cake, then bake for 40-45 minutes or until a skewer poked into the middle comes out clean. Cool completely in the tin.