What type of government was established by the english bill of rights in 1689?

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.