Yes, basically they needed to get out of England due to intense persecution. Quakerism had become a popular social movement and it questioned both the Church of England and the Reformed churches. Quakers, as well as Baptists, emphasized individual and local autonomy--deeply subversive! 1000s of Quakers were in jail during the 1650s through the end of the 1600s. In the 1600s, Quakers believed the "end times" were happening, and George Fox and others believed that Christ had returned inwardly. There was thus no longer any need for churches, priests, or even "Christianity" as it existed.

Not surprisingly, they were banned from the Puritan colonies in the US, but William Penn managed to secure a colony that resulted in PA and freedom for Quakers.

In both England and America, Quakers transformed from being a disruptive apocalyptic social movement into a sober, "quietist" part of society during the 1700s. This was particularly true in PA, where they were the local power establishment and were thus no longer a threat to established authority. In general, during the 1700s Quakers came to focus their ideas on how to live in the long-term, and lost the notion that the "end times" were under way. The idea of "Christ" within was retained, but it was clear that history had not ended.

Check out Ben Pink Dandelion's Introduction to Quakerism to learn about this history.