Proposals to make Church of England schools admit more pupils who do not follow the faith have been widely welcomed.
Calling for a major shake-up of admissions rules, the Rt Rev John Pritchard, Bishop of Oxford, said policies which favour religious children should be changed, even if it affects a school's exam results.
He urged headteachers to reserve no more than 10% of places for youngsters who are practising Anglicans.
In an interview with the Times Educational Supplement, Rev Pritchard, who is chairman of the Church of England's board of education, said: "Every school will have a policy that has a proportion of places for church youngsters... what I would be saying is that number ought to be minimised because our primary function and our privilege is to serve the wider community.
"Ultimately I hope we can get the number of reserved places right down to 10%."
The move would be a major shift for the Church, and it could also lead to an end to the practice of parents attending church to secure their child a school place.
Under current admissions rules faith schools can choose how to allocate places, for example to followers of their faith, if they are over-subscribed.
The Church of England has around 4,800 schools, and the majority are primaries. It is believed that around half of CofE schools are voluntary aided, which means they set their own admissions policies.
Rev Pritchard said he recognised that urging schools to change their admissions policies may not be popular with everyone.
However, the suggestion was welcomed by the National Secular Society, whose president Terry Sanderson said: "The Church has repeatedly denied that the strict selection criteria that are applied in some schools are the reason they perform so well.
"We are told that it is because of the 'Christian ethos'. Now the cat is out of the bag and the Bishop of Oxford has let us know that the Church is fully aware of why their schools perform so well."
He added: "Parents who access these schools won't be too thrilled to see them opened up to the community at large. We've all heard of pushy, non-religious parents suddenly becoming regular church-goers in order to get a letter from the vicar that is the 'open sesame' to the local church school."
Rabbi Dr Jonathan Romain, chair of Accord, which campaigns to end religious discrimination in school staffing and admissions, said: "This is a very welcome step that attempts to help rectify current policy, which means that religion and discrimination in schools have become almost synonymous.
"Schools should be inclusive and tolerant and no state-funded school should be allowed to discriminate on the grounds of religion for any of their teacher posts or any pupil places."
The Church is expected to publish new admissions guidelines in the summer.
Gillean Craig, the vicar of St Mary Abbots Church in Kensington, west London, said he was "incandescent" that the issue of school admissions had been raised on Good Friday.
Speaking to BBC Radio 4's The World At One, he added the idea had not been thought through.
"Today is Good Friday, today the Christian church focuses on the suffering and death of Jesus, and in that it talks about the involvement of God and the suffering and death and agony of our world which presses in on every side," he said.
"The last thing we should be thinking about today is schools admissions.
"So, I am incandescent at the sheer level of incompetence displayed by some senior members of the Church of England who seem to have no idea about how their words will be taken up by the media.
"I feel furious about this."
Asked about the proposal, he added: "I think it's simply not been thought through at all, communities throughout Britain vary enormously.
"In some there are very large numbers of people who worship at a Church of England church, in some areas there is virtually no-one, and I think it's absolutely right that different church schools will reflect that different community that they serve."
Ibrahim Hewitt, spokesman for the Association of Muslim Schools, expressed concern the Church of England was being led by a secularist agenda regarding faith schools.
"The Church of England should be setting a lead and not bending to what is very much a secularist agenda to very much try to get rid of faith schools," he said.
"Church schools and other faith schools should be very clear in saying that people are welcome to come to our schools but we are a faith school, this is the kind of education your children will get.
"If you're happy with that, you're welcome. If you're not happy with that, go to one of the ordinary state schools, of which there are plenty."
Dr Oona Stannard, head of the Catholic Education Service, said they would not be changing their stance on admissions.
Catholic schools were originally set up to "provide an education in the Catholic faith for Catholic children", she said.
Around a third of the pupils who attend Catholic schools are not of the faith, Dr Stannard said, because places are available and families want to take them up, respecting the Church's values.
"Our central purpose of educating Catholic children remains at the forefront of our mission," she said.
"I believe that, through the excellence of the education we provide, and the great popularity of our schools, that the type of education we provide is a service to society."
There are around 2,300 Catholic schools in England.
Kevin Courtney, deputy general secretary of the National Union of Teachers (NUT), welcomed the Bishop's comments and said faith schools should be for the whole community, not just followers of the faith.