I puzzled for months to know what, exactly, constituted the British Constitution. No pun intended.
A ”Constitution” and “Constitutional” before the U.S. Constitution was written, did not necessarily refer to a written document with four corners. Instead, it referred to the rules, written or no, which regulated how laws were made (and therefore could be contained in statutes, albeit special statutes). “Constitutional Reform” was therefore a reorganization of the laws that prescribed how a government worked. “Constitutional History” was, in a way, political history.
The U.S. Constitution essentially revolutionized the modern conception of all things constitutional. Most countries have followed our lead in writing down a Constitution that is intended to be fundamental law which governs longer than the lifespan of most statutes.
Yet Britain's was first. It was lauded by Frenchmen Montesquieu as better than all others in providing for personal and political liberty, and was admired by most Founding Fathers.
I am currently taking/auditing a Constitutional Theory course. It reflects both traditions, in that much of the legal theory derives from U.S. sources, yet the facilitators attempt to apply that theory in a British and international context. I am learning much, especially that you should never tell a British lawyer that Britain doesn't have a constitution...