The Pilgrims, or Brownists, were driven from England- they were a Calvinist sect that was in favor of congregational freedom, for each congregation to decide how to worship. This notion- that there could be more than one church for everyone- was very radical, and they were attacked, jailed, beaten. They fled first to Holland, then to North America.

As far as government, initially the King granted charters to companies who wanted to create colonies, usually for profit. One of the first was the London Company, ( soon changed to the Virginia Company) because the investors were in London. It was chartered in 1606 by King James I and given most all the southern east coast of what's now the US. The Pilgrims were settled by the Plymouth Company ( whose investors were based in Plymouth), which had been given a charter at about the same time to settle most of the land north of the Virginia Company. Other charters followed, for other colonies, like Maryland, Pennsylvania, North Carolina, Georgia. The companies appointed governors , and administered each colony. Those colonies that had been granted charters to a single proprietor were governed by that proprietor- like William Penn in Pennsylvania. All in theory were run in conformity to English law.

However, in the later 17th c. those private charters were mostly surrendered to the Crown, and by mid 18th c. all the colonies were royal ones. From then on, the governors were royal governors, appointed by the King and his ministers, and control of the colonies was directly linked to the British government. But for much of the 17th c. , the colonists had mostly been allowed to govern themselves, and when governors became royal governors, there was always some tension between the governor ( who acted for the Crown) and the colony legislature ( who represented the residents). That tension would grow in the 18th c. as a result of various grievances and become a real revolt.