For the jam: Firstly, place a small plate or saucer into the freezer. Then place the blackberries and sugar into a large wide saucepan and stir together. Place over a medium heat and stir every now and then until the sugar has dissolved and the juice from the blackberries has been released. (This may take 4-5 minutes if you use frozen berries.) Then turn up the heat and boil for 5 minutes. Add a knob of butter to help dissipate any scum, (you can also skim it off with a spoon).
Check the jam is set by removing the saucer from the freezer, and placing a teaspoon of jam onto it. Leave for a minute or so, then drag your finger through the jam. If if wrinkles and leaves a clear line, then the jam is set and you can take it off the heat. If not, continue boiling for a few minutes and check again. Then pour the jam into a heat proof bowl to cool. (You will only need to use 300g of the jam, so you can place the remaining 200g into a sterilised jar. You can sterilise clean washed jars for 15 mins at 150C/130C Fan/Gas Mark 2.)
For the cake: Firstly, grease and flour a Bundt tin and set aside. Then preheat your oven to 175C/155C Fan/Gas Mark 4. In a large bowl, using an electric hand-whisk, cream together the butter and sugar until light and fluffy. Then mix in the eggs one at a time, and then add the vanilla. Combine the flour, baking powder, bicarbonate of soda, salt and cinnamon in a small bowl. Then mix into the batter in 3 increments, alternating with the sour cream between each.
Pour 3/4 of the batter into the prepared tin, and make a little trench in the middle all the way around. Spoon the 300g of jam into the trench evenly, ensuring that the batter (and not the jam) is touching the centre and edge sides of the tin. Then spread the remaining batter carefully over top, so you cannot see the jam anymore. Bake for 50 minutes, until a skewer inserted comes out clean. Then leave the cake to cool in the tin for at least 45 minutes, before removing and placing on a cooling rack to cool completely.
For the icing: Blitz the blackberries in a food processor. Then strain, and discard the seeds and pulp, leaving just the juice behind. Place the icing sugar in a large bowl and stir in the blackberry juice (should be about 45g) until you have a thick icing. Pour icing over cooled cake, so it drips down each side.