In 1661 Charles summoned the parliament and during his reign a series of acts were passed, among them the test act
(a law passed in England in 1673 which prevented Roman Catholics from holding any official public position, including becoming Members of Parliament, studying at a university or joining military forces. The law stated that people had to be members of the Church of England -Anglicans- to do any of these things. It was not cancelled until 1828. )
Charles II's court was the most immoral in English history and when 2 great tragedies took place, the great plague and the fire of London, people interpreted them as god's punishment for his immorality.
A new dutch war broke out in 1668 and England made a triple alliance with Holland and Sweden against France. However Charles II made a secret treat with France in return of some money. They agreed that Charles was to announce his conversion to Catholicism, and the french troops were allowed to enter England in case of opposition.
To avoid the return of a catholic king to the throne, the parliament brought in a bill, the exclusion bill, in 1680, to exclude charles' brother, James, from the throne. So the king decided to dissolve the parliament, and in 1681 another parliament was formed. In this period we see the birth of two parties: the Wigh (supported the exclusion bill) and the Tories (conservatives, supported the king). The bill was passed by the house of commons but rejected by the house of lords. So the succession wasn't modified,but Charles was forced to exile James to Bruxelles. The parliament no longer met during Charle's reign, that ended in 1685.
in 1685 James II came back from his exile. He was catholic (married Mary of Modena in 1660), and attempted to give equal rights to both Catholics and protestants. However the difference between the two religions leaded to conflict with parliament.