‘Nonconformists’ in the context of English Church History refers, strictly speaking, to denominations that were formed after the 1662 Act of Uniformity, which required all clergy to use only the Book of Common Prayer in worship. Over 2000 ministers refused to conform to this, leading to the “Great Ejection”. In due course these and others formed Nonconformist Denominations such as the Presbyterians, Congregationalists and Baptists. From that time onward church bodies were either Church of England or Nonconformist. Until the Act of Toleration under William and Mary there was outright persecution of Nonconformists, and there were certain restrictions of rights until the early nineteenth century.
However, in a broader sense Christian Nonconformity in England goes back at least to Wyclif, who in the fourteenth century refused to conform to certain non-biblical doctrines of the Roman Catholic Church. Until the Reformation began in Germany in 1517, Nonconformity was generally a matter of individuals committing themselves (usually, but not always, in a quiet way) to the authority of the Bible over that of the Pope (or later, the king). They were Nonconformists because they were officially heretics if they believed this way, declared so by an act of Parliament in 1401.
After 1517 we read of groups of scholars at the universities, especially Cambridge, gathering together to read and discuss Luther’s writings and later preaching these doctrines which did not conform to the official doctrines of the emerging Church of England. However, it was during Elizabeth’s reign that underground congregations began to form in London. These had different systems of church government than the state church, primarily Reformed or Presbyterian and Separatist. In 1593 an ‘Act Against Puritans’ was passed, stipulating that anyone who failed to attend an approved church and instead worshipped with a ‘conventicle’ (underground church) ‘shall be committed to prison, there to remain without bail... until they shall conform’. From this time until 1640, when the Puritans gained the upper hand in Parliament, these bodies were suppressed. Between 1640 and 1660 it was the Episcopalian system that was suppressed.