Mix all of the ingredients together along with a pinch of salt, then tip into a freezer-proof container and freeze overnight.
The next day, defrost the mixture in the fridge until the blackberries are soft (this will take about an hour). Tip the defrosted mixture into a high-powered blender and whizz until completely smooth. Pour into a jug through a fine mesh sieve, then put in an ice cream machine and churn and freeze following manufacturer’s instructions. Scoop the sorbet into bowls to serve.