"...a restraint designed to allow an owner to keep a pet dog under control whilst allowing the dog a limited amount of freedom to follow its natural instincts..."

Well I think that a good dog owner should be able to keep their dog under control at all times without resort to a lead. A dog can be trained to walk to heel and stay close to its owner. Sticking a lead on it, whether a long or short one, is a sign that the dog is not under your full control. Of. course, it could also be because there's a by-law in force, a law that would be unnecessary were all dog owners required to be in full control of their animals.