There is a difference between Church of England schools and Roman Catholic, Jewish and other faith schools. The latter were set up to provide education specifically for children of Roman Catholics, Jews and so on; whereas Church of England schools were set up to provide education for all children living in a parish -- that is, the geographical area within the parish boundaries. They were specifically not set up just to provide education for the children of church-going families. Indeed, let us not forget that before the state was involved in education, churches (and especially the Church of England) set up schools for the children of those who could not pay for education. It was only Christians who thought the children of the poor worth educating.
The reason that Church of England schools select is not because they wish to have only Christian children: far from it. Selection was forced on them by the introduction (in the Thatcher years) of the right of parents to send their child to any school regardless of catchment aka the introduction of parental choice coupled with the introduction of league tables and publicly-available Ofsted ratings. This has created a market in education in which "better" schools are oversubscribed and are forced to select, and where schools have become increasingly segregated by class. It is in this situation that Church of England schools have used the Church membership selection criterion. And we need to remember that this is a situation that is specific to urban areas (especially London) where pressure on school places and anxiety on the part of aspirant middle-class parents is intense. Many Church of England schools never use the church membership criterion and admit all children in the catchment regardless of faith. They act as community schools in exactly the same way as county schools. In my city, as it happens, the schools that people fight to get into are not the Church of England schools -- these overwhelmingly serve areas of deprivation and are much less desirable.
The 10% of capital costs that the Church of England contributes is far from negligible, especially considering that the Church of England has been involved in rebuilding many older schools and in new building projects. When we consider that that money is generated entirely from voluntary contributions by church-goers, it is a very large subsidy to state education, which, given the parlous state of local authority finances, would be impossible to make up from either central government grants or from local tax receipts. And, of course, the trustees of Church of England schools also own the land on which the school is built -- that is another enormous capital investment that would be impossible to buy out.
But the issue isn't really about the investment that the Church of England has put into schools, or its noble history as a pioneer of education for poor children. It's about fear of religion: so much of what is evidenced in these threads is fear of what these Christians might do to our children if they got their hands on them; how our children's minds might be poisoned by their evil dogma; how our children might be forced to pray and punished if they do not; how our own secularist and atheist values might be undermined by religious teaching. In the end, it comes down to a fear that our children might be converted.
Interestingly, these are some of the things that people used to fear about gay people. Now, thankfully, most people don't have these fearful and silly ideas that their children will be converted by contact with gay people. But prejudice doesn't simply go away, it seems, but migrates to a new object. I don't think Christians are persecuted in this country (although violence against visible Christians is under-reported). But as people have less and less contact with Christianity and many people nowadays simply do not know any Christians, nor have they ever been in a church prejudice against Christians has grown. We all know that prejudice is fuelled not by familiarity but by ignorance. We know that when people know gay men and women, and know them as people, their irrational fears subside; we know that racism is more prevalent in areas where there are few black people; we know that anti-semitism flourishes where there are legal restrictions on the right of Jews to settle and to practise their religion.
In this sense, I would make an argument that the provision of Christian worship in schools is the best defence we have against prejudice and fear. The essence of Christianity is not doctrine but worship and prayer. You do not have to join in (indeed it is impossible to make anybody assent internally to anything they don't want to you can look as if you are praying and inside be having any kind of thoughts you like). But sharing in other people's experience, and learning what it is like to be in their shoes, and finding out through experience what is good and what is bad about what they do that is the foundation of understanding and shared humanity. I would be more than happy for my children to share in Muslim, Jewish or Hindu worship, and I'm not worried that my children's minds will be poisoned by it, or that they will be converted, or any other horrid thing. The truth is that they will be more influenced by what their friends and peer-groups do and think and say than anything that happens at school.