Preheat oven to 350F or gas mark 4 and place cupcake liners in the cupcake tin.
Whisk the flour, baking soda, baking powder and salt and then sift into a large bowl and set aside.
On medium high speed, cream the butter and sugar until light. Then add the lemon zest and eggs.
Reduce the speed to low and add half of the flour mixture, mix until just incorporated, then add the buttermilk and lemon juice mixing until just combined, and follow up with the remaining flour mixture.
Fill cupcake papers about 2/3 the way up. Bake for 15-18 minutes or until the springy to the touch.
Making the Blackberry Buttercream:
Ina saucepan heat the blackberries and lemon juice until the blackberries release their liquid and comes to a boil. Strain with a fine mesh sieve and allow to cool.
Cream the butter and salt for a few minutes then sift in the powdered sugar in a few batches, mixing in between. Add the cooled blackberry liquid and mix until combined. Scrape down and to a piping bag and decorate the cooled cupcakes.