The rise of Puritanism is a key factor in the decline of drama in England after Shakespeare. The Puritans were fanatical Protestants who regarded the theatre and other forms of entertainment as sinful, so they were always trying to get theatres closed down.
Although Puritans were around in Shakespeare's day, Queen Elizabeth kept them in check, and so English theatre thrived during her reign. However, under later monarchs, Puritans become more powerful and important in public life, giving them a greater degree of control over what people could or couldn't do.
Not long after the outbreak of the English Civil War, the Puritan-dominated Long Parliament closed down all the theaters in London. Then as now, London was the epicenter of English theatre, and so the closing down of theatres had a catastrophic effect on drama in the land of Shakespeare, Marlowe, and Jonson.
Theatres would remain closed until the restoration of the monarchy in 1660. The ascension to the throne of Charles II, a notable patron of the theatrical arts, brought about something of a renaissance in English drama, most notably in the field of comedy, with playwrights such as John Lacy and George Etheridge capturing the public mood for humor and frivolity after years of Puritanical repression.