This is such a bugbear of mine as my children are not Christian.
For info - the required contribution from the Church is 10% of capital costs only not running costs (running costs are paid through the payment for each child by the state).
"Before the Education Act 1944, voluntary schools were those associated with a foundation, usually a religious group. The Act introduced two categories of maintained voluntary school:
? Voluntary-controlled (VC). These had all their costs met by the state, but were controlled by the local authority.
? Voluntary-aided (VA). These were partly funded by the state, with the foundation responsible for 50 per cent of capital works and having greater influence over the school. The 50 per cent figure has subsequently been reduced to 10 per cent, although the local authority does have discretion to cover this."
www.education.gov.uk/schools/leadership/typesofschools/maintained/b00198369/voluntary-and-faith-schools
So for 10% of the capital costs they get to control most of the places in the school.
As for why faith schools get better results below are some details about my local primary schools (3 closest faith & 3 closest non-faith) spot the difference 
"Here is an illustration of how choice doesn't really work fairly in the state sector. These are primary schools close to where we live in London all within 10-15 mins walk of each other.
Why is it that the faith schools have lower numbers of both English as Second Language (ESL) and children eligible for free school meals (FSM).
Faith School1 - ESL 67.2% FSM 35.2% (Children acheiving L4 81% L5 19%)
Faith School2 - ESL 34.9% FSM 14.4% (96% / 58%)
Faith School3 - ESL 58.1% FSM 8.5% (93% /58%)
Community School1 - ESL 76.8% FSM 50.2% (76% / 14%)
Community School2 - ESL 81.3% FSM 49.3% (82% / 5%)
Community School3 - ESL 87.5% FSM 58.5% (67% /18%)"