The three elements noted above fall under the rubric of constitutionalism. Medieval political structures were constitutional but failed to have an effective means of enforcement short of revolution. Kings were bound to uphold the rule of law and protect their subjects' liberties but there wasn't much anyone could do about a king who failed on either or both counts.
The Reformation and the aftermath of the English Civil War created in seventeenth-century England new sub-revolutionary means of redressing the rights of subjects. These means included trial by jury (where jurors were impartial rather than witnesses), the rudiments of rules of evidence which allowed for the first time parties to testify in civil matters, and, most important, Parliamentary supremacy culminating in the English Bill of Rights.
(For more on the law of the century before and the some of the legal effects of Puritanism and the English Civil War, download my article The Puritan Revolution and the Law of Contracts here. It may be the only article published in a law review that considers questions from the Westminster Larger Catechism.)
The latter was of signal importance in Puritan New England, the one place in the Colonies that had sought to establish a biblical Christian commonwealth, not an extension of Protestant England. With Parliamentary supremacy came the revocation of the original royal charters. Most interesting, however, was the sudden change of heart by the Mathers. Deprived of the opportunity to continue the experiment of creating a biblical commonwealth (an experiment that wasn't going very well anyway), Increase and Cotton Mather switched gears and made a virtue of necessity. It was no longer a godly society but a British constitutional one that was at the telos of political life.
Thus even for Puritan New England--as it had always been in the rest of the colonies--it was British constitutionalism that made the American experiment unique. While British constitutionalism was politically and religiously (but only broadly) Protestant, it was not biblical in the narrow understanding that pervades much contemporary "Christian America" thought.