As a recently retired solicitor, Enfieldspares has got it right.
On formerly ancient common land -i.e not in any single person's ownership, those with rights in common had the right to e.g graze animals and take rabbits and wildfowl etc, so a common right holder would have had a right in effect to hunt on that land. The few remaining commons ( many were taken into private ownership by wealthy landowners via Enclosure Acts up to and including the 19th century - English equivalent of the Highland Clearances but we English don't seem to have a grudge about it still!) have been registered in the last few decades under the Commons Registration Act - quite a few in East Anglia remain where registered rights holders use the right to wildfowl. This might charitably be the cause of the apparent confusion - nothing as such to do with the "common law" as lawyers know it, but perhaps everything to do with rights of commoners over their common land.