In a food processor, whizz together the berries, sugar and pomegranate juice until smooth. With the motor still running, gradually add the cream and continue to whizz until well blended. Transfer the mixture to a stainless steel bowl, cover with clingfilm and put in the freezer.
Freeze the sorbet for an hour until set. Take the bowl out of the freezer at 15 minute intervals to whip the mixture with a spatula. Remove from the freezer 5 minutes before serving.