Definitions for "Non-Conformist"
a general term for those who do not assent to the Established Church. Much the same as Dissenter, but the word is much more negative. The sequence Puritan - Dissenter - Nonconformist is significant of a decline in intensity.
church that is not Church of England (they were founded by people who would not conform to the 1662 Act of Uniformity)
Someone or something (like an institution) which does not follow the established church, in this case the Church of England.