Cream together the butter and sugar using an electric whisk.
Whisk together eggs and milk in a jug. Get the flour and baking powder ready in another bowl.
Add some of the egg and milk mixture to the butter and sugar, followed by some of the flour mixture, and mix well. Keep adding until it is all in.
Add the zest of the lemon and stir.
Grease your slow cooker pot and put in a cake case or baking paper.
Put half the cake mixture in, then put in the puréed blackberries.
Add the rest of the cake mixture on top and swirl slightly.
Cook for 1-2 hrs on high (see notes above) or until a skewer comes out clean.
Remove from the pot when it has cooled enough to handle, and allow it to cool fully on a rack. This will take quite a while.
Once it is completely cool you can ice it if you want to (or just eat it up!). I topped mine with blueberry buttercream made with 150 g butter, softened, and approx. 300 g icing sugar, whizzed up using the electric whisk. I microwaved a handful of blueberries in a little water for a minute on high, then left it to cool and removed the skins. Then I stirred the juice into the buttercream little by little to achieve the desired colour.