On Sunday, GAFCON UK released a report in which clergy known to be in same-sex relationships or who have officiated over same-sex marriages were named.
On the group's website, it says the report was handed out at a briefing of conservative bishops in order to highlight that the Church of England has already "crossed the line" in its acceptance of homosexuality.
The report lists a number of "violations" of the Church's ban on same-sex marriages, laid out in the Lambeth 1.10 resolution.
The Lambeth 1.10 resolution was passed in 1998 and upholds the belief that marriage should be between a man and a woman.
The GAFCON report was released ahead of a meeting of Church of England bishops in which the Church's position on gay marriage will be discussed.
The report concluded that: "To restore order and a credible Christian witness, the upcoming meetings of the House of Bishops and General Synod would need to not merely avoid going further in violating Lambeth 1.10, but it would need to take constructive steps to rectify the numerous public (and presumably private) breaches that have been strategically taken by some to undermine the teaching of the Communion."
Canon Jeremy Pemberton who is married to another man, is among clergy listed in the document.
On Monday Canon Pemberton tweeted: "Handy guide to everyone out and proud in the C of E. "Violators of Lambeth 1:10" #nastypeople"
Andy Lines, the Chairman of the GAFCON UK Task Force, defended the group's decision to publish the list of names of gay clergy.
Mr Lines told Premier: "GAFCON UK has been consistent in setting out the need for all churches to clearly and graciously commend the Bible's teaching on sex and marriage, and to resist efforts to change this teaching or to ignore it in its practice in parishes.
"The list of clergy and bishops is not designed to 'name and shame' anybody. GAFCON UK opposes any form of homophobic abuse. The [names of clergy] are in the public sphere, often publicised by the people themselves. GAFCON UK is merely collating a report which lays out the Lambeth 1:10 position and explains how Western, liberal Anglican Provinces have violated these guidelines."
Same sex marriage has been legal in Scotland, England and Wales since 2014.
Premier has reached out to the Church of England for comment.