Common law
The common lawso named because it was "common" to all the king's courts across Englandoriginated in the practices of the courts of the English kings in the centuries following the Norman Conquest in 1066. Prior to the Norman Conquest, much of England's legal business took place in the local folk courts of its various shires and hundreds. A variety of other individual courts also existed across the land: urban boroughs and merchant fairs held their own courts, as did the universities of Oxford and Cambridge, and large landholders also held their own manorial and seigniorial courts as needed. Additionally, the Catholic Church operated its own court system that adjudicated issues of canon law.
By-law
The Merriam-Webster Dictionary indicates that the origin of the word by-law is from the English word "bilawe", probably from Old Norse "*bȳlǫg", from Old Norse "bȳr" town + "lag-, lǫg" law. The earliest use of the term, which originates from the Viking town law in the Danelaw, wherein "by" is the Old Norse word for a larger settlement as in Whitby and Derby (compare with the modern Danish-Norwegian word "by" meaning town, or the modern Swedish word "by", meaning village). However, it is also possible that this usage was forgotten and the word was "reinvented" in modern times through the use of the adverbial prefix "by-" giving the meaning of subsidiary law or side-law (as in "byway"). In either case, it is incorrect to claim that the origin of the word is simply the prepositional phrase "by law."