Deism, or Christianity without Christ
To promote toleration within the Anglican Church, Locke and other Whigs argued that further religious conflict could be avoided if everyone could agree on a basic, minimum set of beliefs necessary for someone to be a Christian, beginning with the belief in God. Beyond these minimum beliefs, they said, reasonable people could differ without becoming fanatics who had to have everyone agree with them. Because it emphasized the belief in God over any belief in Christ or the Bible, this movement (composed primarily of members of Anglican Church, not radicals) was called Deism.
Deists proposed that people should know about God through study of nature, from which they could learn not only physical laws of the universe, such as gravity, but spiritual laws as about how to live properly. They emphasized that all beliefs, including religious beliefs, should come directly from human reason (which meant the clergy would not be necessary to interpret for people). Deists called this idea "natural theology" -- that God had created Nature and then withdrawn from the world, leaving humans to make it on their own.
In Britain, this was not at all a radical movement like the Puritans had been; it drew generally well-off and well-educated members of the gentry who prided themselves on knowing how to act and to speak and write like a gentleman, that is "politely." So Deists did not attack the clergy or make a crusade out of their natural theology. Nevertheless, this amounted to a serious challenge to organized religion (i.e., the Anglican Church) since it called for nothing but reason and belief in God. None of its adherents questioned the existence of God; Deism was not atheism.