From Keith E. Wrightson's Yale course on Early Modern England. Puritans can usefully be thought of as Protestant fundamentalists, the equivalent of today's extremist Muslim popular movements, advocating the permeation of a 17th-c. Christian sharia throughout all aspects of social and political life. They were revolutionaries all right, but rather in the line of Christian Ayatollahs. And revolutions, not to forget, are usually led by an elite seeking power, in this case a middle-class elite.
With the triumph of the Revolution, much of the everyday life of the English came to be dominated by this Puritan mixture of Thought Police and Sin Police, and it is perhaps a negative reaction to this tyrannical invasion of privacy and everyday life, rather than an active passion for the monarchy, that explains the widespread relief at the Restoration of the Stuarts.