Apparently 1 million children attend Church of England schools. A quarter of all primary schools and 6% of secondary schools are Church of England schools.
Around 15% of the population attend a church at least once a month, according to research reported here, although figures of between 10-12% are also reported. The total UK population is 63.7 million, so the number of people who attend any Christian church is somewhere between 6.3 and 9.45 million. However, it needs to be borne in mind that the average age of church attenders is now between 50 and 60.
The number of young people under 18 in the UK is 13 million, of whom 6.1 are under 13. The number of children educated in Church of England schools (just under 10% of the total, but more like one seventh of those of primary age, because most CofE schools are primary schools) far exceeds the number of children who attend church. (Don't forget, all families who attend church to satisfy an admissions criterion will be counted in the church attendance figures.)
It cannot be the case, then, that Church of England schools are only admitting the children of church-going Christians. In fact, the reverse is true: that overwhelmingly Church of England schools are serving the communities of which they are a part, as they were set up to do.