If Bentham posited a sense of guilt as pain that most would feel when doing wrong by others, then surely Utilitarianism would be unnecessary due to Bentham's own work on the motivation of human beings.
Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do.
If Bentham were to maintain this view whilst considering a sense of guilt as pain then wouldn't we naturally behave in a morally permissible way?