The response comes after GAFCON, which represents a wing of the church which adheres to traditional teachings on issues such as women in ministry and sexuality, published a letter which criticised the Church of England because it has allegedly "crossed the line" by allowing some of its clergy to either bless same-sex relationships or be in them themselves.
GAFCON said the letter was published "with permission" and it cited decisions made at the Lambeth Conference 1998 regarding sexuality which it argued the Church of England is continually allowing to be broken.
The group's letter then proceeded to name clergy and other groups linked to the Church of England that it deemed to be contravening rules on sexuality.
GAFCON has said identifying individuals was not meant to shame them, but one of those named called them "nasty people" for doing so.
The Church of England reminded GAFCON that:
"Clergy in the Church of England are indeed permitted to enter into civil partnerships (which are legally not the same as marriage, and therefore have no bearing on the doctrine of marriage)."
"Clergy in the Church of England are permitted to offer prayers of support on a pastoral basis for people in same-sex relationships."
"Churches are able to indicate that they welcome LGBTI people, just as they would welcome all people."
"Clergy and laity are entitled to argue for changes to teaching and practice."
In response William Nye, Secretary General of the Archbishops' Council, said: "The paper paints a significantly misleading picture both of the teaching and practice of the Church of England, and of Resolution 1:10 of the 1998 Lambeth Conference. I am writing to correct some of the erroneous assertions.
"You describe a number of issues as being "violations"... For many of these, I would venture to suggest that they are not "violations".
"When the Government proposed to introduce same-sex (civil) marriage the Church of England argued against it, including in Parliament.
"It is not the case that no discipline has been applied to clergy who, in violation of their duties under the Canons, have entered same-sex civil marriages. How discipline in the Church of England is applied is a matter for the Bishops of the Church.
"At present, the House of Bishops is reflecting on conversations across the Church on same-sex issues. But at this point no change has been made to teaching, nor has there been any formal proposal to do so."