This is the description applied to Protestant church denominations, which historically rejected the teachings and legal requirements of the Church of England. Many prefer to be called Free churches, which signifies that they are free from state control.
In English history, a non-conformist is any member of a Protestant congregation not affiliated with the Church of England. The earliest non-conformist groups included Presbyterians, Independents (Congregationalists), Baptists, and Quakers. Later non-Conformists included Methodists and the Salvation Army.