What's important about Edmund Plowden's Reports is that he collects and expounds on the legal argument behind the king's two bodies, which is an older more medieval and mystical concept and not one cooked up in Plowden's day. (PS - You can get Volume 1 of Plowden's Commentaries or Reports free on Google Books. I love Google Books.) The Elizabethan culture was clearly concerned with legal questions of kingship, how do we define it, how do we define the body of a king -- or queen, for that matter, how do we deal with the assumption that a king's body is different from that of a common man. These questions are not just tackled in medieval and renaissance courts, but the very questions tackled in Shakespeare's history plays.
Plowden was 46 years old when Shakespeare was born, so they were not of the same generation. Shakespeare would likely have been familiar with Plowden's work though, given his own interest in the law and activity in the English courts. Kantorowicz pulls several passages from Richard II to show how Shakespeare is thinking in terms of the king's two bodies through the character of Richard. Here's a snippet from Plowden's Reports which opens up both The King's Two Bodies and Richard II, and I can't wait to dig in further.
For the King has in him two Bodies, a Body natural, and a Body politic. His Body natural (if it be considered in itself) is a Body mortal, subject to all Infirmities that come by Nature or Accident, to the Imbecility of Infancy or old Age, and to the like Defects that happen to the natural Bodies of other People. But his Body politic is a Body that cannot be seen or handles, consisting of Policy and Government, and constituted for the Direction of the People, and the Management of the public weal, and this Body is utterly void of Infancy, and old Age, and other natural Defects and Imbecilities, which the Body natural is subject to, and for this Cause, what the King does in his Body politic, cannot be invalidated or frustrated by an Disability in his natural Body.
(Kantorowicz, Ernst H. The King's Two Bodies. Princeton: Princeton UP, 1957. Book. From page 7, citing Plowden's Commentaries or Reports published London, 1816, page 212a.)