That's a very simplified view. The Puritans were persecuted but they weren't exactly a tolerant group themselves. The majority of the English weren't Puritan. The exodus began before Cromwell came to power but the conflict came to a head under his rule. He banned inns (pubs), theatres, sport, etc. The best example of his intolerance towards other Christian denominations was his treatment of Irish Catholics. Cromwell invaded Ireland and slaughtered entire towns. He also oversaw the imposition of the Penal Laws. Catholics were effectively banned from participating in society. The English hated Cromwell and his rule signalled the end of Puritanism in England.