A perspective.
Britain doesn't have a written constitution because it's traditions supersede one.
Imperial Rome endured and prospered for 1,000 years fostering the attitudes,
instincts, sensibilities and virtues that birthed Europe; which was ruled by Monarchy
till the French Enlightenment. As such Constitutionalism was largely irrelevant.
Britain had developed and embraced strong traditional precepts from its earliest
days. Additionally it is separated from the continent by the Channel which
largely shielded it from the chaos and unrest spawned by the French revolutionaries.
In effect, Britain has no need of a written document.