They have written an open letter to The Guardian newspaper, which said some parents are going to church when they normally would not, to get their child into a good school. This in turn makes Church of England attendance figures look bigger than they really are.
The letter said because Christian pupils are often from more wealthy backgrounds, the school's achievements are boosted. The signatories think Church of England schools are "turned to the advantage of those who are already advantaged."
The full letter, signed by clergy, theologians, experts and MPs, can be read here.
One of the signatories, Revd Stephen Terry from the Parish of Aldrington in Hove, told Premier's News Hour: "My particular problem with the current situation is that it doesn't give everybody a level playing field.
"I have no objection to faith schools, but I do think they should be open to all without qualification and without selection.
"This is an unfair way of proceeding, we should open our Church of England schools to anyone who wishes to send their child, and have an open selection, and inclusive selection policy which reflects this.
"On grounds of natural justice and pure fairness, we feel this is the right way forward."
The Church of England's Board of Education and The National Society, which is part of the Anglican Church's school work, issues guidelines on admissions policy to the 41 dioceses. These dioceses in turn issue admissions guidance to CofE schools located within them, which each have different admissions policies.
Not all Church of England primary schools have a faith-based selection policy, and the extent to which a potential student's faith background is considered varies from school to school. Some Anglican schools only prefer Christian candidates when they are over-subscribed.
Premier has contacted the Church of England and is waiting for a response.
Listen to Rev Stephen Terry speaking to Premier's Hannah Tooley on the News Hour: