Combine chicken stock, blackberries, jam and red wine vinegar in a blender; process until smooth. Run through a sieve to remove seeds, if desired. Pour into a large bowl and set aside.
Heat the oil in a frying pan over medium-high heat. Sear pork on all sides to brown and remove from pan. Pierce meat with a fork every 2cm; place in bowl with blackberry sauce. Cover and chill in the fridge for at least 12 hours, turning occasionally.
Preheat the oven to 180 C / Gas 4. Remove pork from marinade, pat dry and transfer to a roasting tin.
Roast in the preheated oven uncovered, about 1 hour or until internal temperature measured with a meat thermometer reaches 70 degrees C. Remove from oven, and let rest about 10 minutes before slicing to serve.
While the pork is roasting, transfer marinade to a saucepan. Bring to the boil and add rosemary. Boil over medium-high heat until sauce has reduced and thickened slightly, about 10 minutes. Serve sauce over sliced pork.