Church of England schools are struggling to recruit Christian head teachers.
Around one million children attend Church of England schools, made up of around 4,500 primaries and more than 200 secondary schools, many of which are led by heads who do not consider themselves to be practising Christians.
Rev Nigel Genders, the Church of England's chief education officer, said parents want to send their children to them "because they recognise in them something of the broad vision that we have for education".
But he said a lack of effective leadership training for heads has led to the launch of a large-scale consultation about how to improve this.
Heads and teachers alike have also said they want more help and better training to enable them to promote the Church of England's vision for education.
Mr Genders said: "Church schools continue to be oversubscribed and popular with parents and pupils, opting for a Christian-based education whatever their own faith.
"Both community and church schools increasingly testify to difficulties in recruiting headteachers and our recent consultation has shown a strong desire for more support in training new leaders.
"They say that the training that they're provided with doesn't always help them to focus on those broader issues, that it tends to be narrowed to just thinking about particular things which they will be held accountable for rather than this broader vision for a hugely diverse and encouraging education, which they can give to all of their children."
He said Church of England schools are "about allowing children to really flourish".
"What we want is for all schools to be able have access to that kind of education and that richer, deeper, broader curriculum," he added.