Earlier this month, the Church issued a documents encouraging clergy to use liturgy "to enable people to mark a major transition in their lives".
The guidance suggests a person can renew the commitments they made in baptism in a public setting marking their new identity.
The Church said water or oil could be used in the service which should be "celebratory" in nature.
According to the Sunday Times, a number of bishops, led by Bishop of Wakefield Rt Rev Tony Robinson, are now said to be calling for a conscience clause to be introduced for those who feel they couldn't lead a service like this.
The original guidance was released with a commendation from Bishop of Blackburn Rt Rev Julian Henderson.
He initially said: "This new guidance provides an opportunity, rooted in scripture, to enable trans people who have 'come to Christ as the way, the truth and the life', to mark their transition in the presence of their Church family which is the body of Christ."
However Bishop Julian later released a second statement as part of the Church of England Evangelical Council, contradictory to the first, in which he warned the guidance was "both highly divisive and theologically and pastorally questionable."
The Church of England says there is no obligation on clergy to offer this service.
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