80% of those who migrated to New England during the Great Migration did so between 1633 and 1640 due to Archbishop Laud’s relentless persecution of Puritans.1
The Massachusetts Bay Company, however, was not established due to religious persecution.
Instead, it formed due to socio-economic factors that included: emerging colonial trade, increased social mobility, and the Thirty Years War. As political unrest and religious strife tore the fabric of early 17th Century English society, family and social ties forged alliances that held it together. One such alliance resurrected the defunct Dorchester Company to form the New England Company, which then morphed into the Massachusetts Bay Company.
1 Anderson, R. C. The Winthrop Fleet. (New England Historic Genealogical Society, 2012). P10