The process of royal authority being curtailed began with King John's signing of the Magna Carta in 1215 in the Middle Ages, a monumental legal document which outlined the rights and responsibilities of the king and his peers. (The barons had actually rebelled because they felt John had infringed on their rights as nobles. John granting concessions was the aftermath of their feud.) This would lead to a slow and gradual devolution of political power from the throne to parliament.
Charles I believed in the divine right of kings and wanted to exercise royal authority (what is still called the Royal Prerogative) as if he was accountable to no one. This incensed the English parliament, who insisted that actual political authority remained with parliament and acted in the king's name. This dispute led to the English Civil War 1642-51 between Parliamentarians and Royalists, Charles' dethroning and beheading, and the interregnum period when Oliver Cromwell ruled England. Charles II restored the monarchy, but it was one now formally limited by, and accountable to, parliament.
It should be noted that the monarch always has this royal prerogative, which on paper appears to represent great authority. But over the centuries of evolution of legal processes and tradition in England (and later, Britain), royal authority became more symbolic than actual power. The king has tremendous symbolic authority, but it is always exercised "with the consent of Parliament". This principle is sacrosanct in Britain and Commonwealth countries where the UK monarch is head of state.
The king cannot, in principle, do anything without first consulting the government acting in his name. In reality, the Privy Council -- the prime minister and cabinet ministers who "advise" the king -- holds the real power in the modern Westminster parliamentary system, even though they take an oath to the king. They write and create bills that the king out of tradition gives royal assent to, making them into laws. He must give assent in other words, despite his royal prerogative to reject laws, or dismiss the prime minister and his government. This system of government -- a constitutional monarchy -- hinges on the monarch abiding by this and the elected government "advising" the king and both parties honouring this symbiotic relationship.
To do otherwise, for example the king deciding arbitrarily to dismiss the government without first seeking advice from the PM, would create a constitutional crisis. And every English royal since Charles I remembers the last time that a king challenged the parliament's authority -- he lost his throne ... and his head.