Whilst the whole thing is an accident of history, it's plain from reading this forum that church schools are something of a blight on some people's lives. As has been said, the CofE was responsible for setting up many schools, as was the Catholic Church and for a long time they have been given money from taxation to do this. County/community schools were built to fill the gaps where church schools did not exist. And therein lies the problem.
I'm in a semi-rural area with a small market town. Every village has a Victorian CofE school. There is even one in a parish that only has 30 or so houses within walking distance of the school. The nearest town only has 1 CofE school too - and in the 70s it got so crowded that they created separate infant and junior schools on 2 sites. So the rest of the schools in the town were built by the LEA as the town expanded. 1 in the town centre in the 1920s. 2 in the 50s in the middle of a large council housing estates. 2 in the 60s - 1 in a council estate the other in the middle of a new estate of private housing. 1 in the 70s on a large housing estate where one side of the road was council and the other private housing - the school on the council estate side. There is also a RC school.
Fast forward to when we moved here in the early 90s. Many of the homes in the 1950s and 60s housing estates are now privately owned. The 70s housing estate (council side of the road) is a real problem area with lots of crime and drug use. We know know due to league tables that the school in the middle of the private housing estate has the "best" results - the one in the 70s has the "worst" results. Whilst the 70s schools was built for 2 form entry, not many people want to send their children there. All other town schools full. RC school also full - due to non-RC children whose families do not want them to be at 70s school. The village schools do really well - but of course, they are CofE schools! NB: It costs a lot of money to buy a house in a village and the new houses in villages are generally "executive" homes. Parents at the edge of town who prefer their children to go to "good" schools (and who do not depend on public transport) can drive children to village schools. This is also possible if they live on 70s estate, although things get more tricky as all the other schools get fuller and the 70s school gets emptier.
Another decade passes - Labour Govt has lots of money for schools! The 70s school in town still a disaster - special measures/new HT/freshstart/new HT/special measures/new HT ... But never mind because the village schools can get lots of money from the govt to build new classrooms. Even the village school in the tiny hamlet can now cater for 60 children and carloads are being transported through country lanes so they don't have to go to 70s school. Parents at village school up in arms about the 60mph speed limit outside the school. Council tells them there have to be 10 houses in a row before speed limits can be lowered ...
You couldn't make this up.
Whilst I appreciate this is a different issue to those of you living in London, I think the root cause is the same. I think the evidence that Church schools as a collective group do "better" is as much from the fact that in the main, their locations are not representative of England as a whole as it is from the fact that their "ethos" is different. It's almost like a self-perpetuating myth. In our area if you live in a village, the only choice is a CofE school. If you live in the town, unless you live next door to it, not have no chance of getting into the CofE school - even if you wanted to.
I think that everything Gove is doing is going to make the situation worse rather than better. He is clearly afer getting rid of LAs altogether, at which point it will be nobody's job to make sure there are enough schools in sensible locations. But hey ho.