They were called Separatists.
This group separatists fled England because they felt persecuted by the Church of England. Just like others who refused the follow the church's teachings at the time, they were harassed, sent to jail, and at times fined. When they could not take it anymore, they opted to flee to Holland where they sojourned for 12 years.
After 12 years they moved to America and established the Plymouth colony in New England. They had felt they were losing their English identity due to the Dutch lifestyle and together with fear of outbreak of war between the Dutch and Spanish, they were prompted to escape to America.