constitutional monarchy:

England is a constiutional monarchy, that is the king or queen is a largely ceremonial position and acts as the head of state. The monarch can grant honors and formally appoints the prime minister (and in a hung parliament, could theoretically select the prime minister) and fomally summons and dissolves parliament. Documents such as the Magna Carta in 1215 and the English Bill of Rights in 1689 gradually reduced the monarch’s power. The monarch has certain “prerogatives” that have largely gone unexercised in modern times.

Incidentally, there is no such thing as the British constitution. It is mixture of common law and those documents mentioned previously that collectively are a de facto constitution.