Question

How did the Bill of Rights legally change the political system in England?

Answer 1

I believe the answer is: It introduced a constitutional monarchy.

In a constitutional monarchy, the country would be still ruled by Kings or Queens. But, in normal monarchy, the Kings and Queens had the absolute power to create whatever laws they want and had the powers to execute any people who displeased them.

In a constitutional monarchy on the other hand, the absolute power is held by the Law, and every actions made by the Kings and Queens shall not contradict the rules that written on the Law.

Answer 2

It introduced a constitutional monarchy.

The Glorious Revolution of 1688 deposed King James II and replaced him with his daughter Mary and her husband William of Orange, the Stadholder (leader) of the Dutch Republic.  As king and queen they became William III and Mary II of England.

James II had tried to take back power away from Parliament.  William and Mary were willing to sign the Bill of Rights as they came into the rulership of England, which guaranteed parliamentary rights that needed to be respected by the monarchs. This meant, in effect, a constitutional monarchy, where the power of the monarchs was limited by the Bill of Rights that protected the authority of Parliament.