I can see that this discussion has moved on a lot since I last posted, it has been very interesting reading.
With regards to Catholic schools, I can only speak from my experience of getting my dc into a Catholic school where we live, a in a reasonably affluent London borough. All the church schools, Catholic or CofE in our area are heavily oversubscribed, as are the state schools. There is also many private schools in my neighbour hood, and a few relatively good state schools. Our dc was number 65 on the waiting list for the local state school, which means that they would have to fill two more classes for my child to get a place.
Looking at the prospectus for the Faith schools, they all state that first priority is siblings of children already in the school, second is faith and active life in the church, thereafter baptizm, further geographic proximity to the school and finally other religious beliefs.
So in theory other beliefs are welcome, but in reality when the siblings and the children of active church goers have been offered a place, there may only be one or two, or maybe no place for geographic proximity and further down on the list.
My husband is Catholic, our dcs are baptized Catholic, I am very active in my local CofE Church, doing lots of voluntary work, so we had the choice of either.
Our dc was offered a place in a very good Catholic school in the neighbouring borough (its a trek in the morning but worth it if he gets a good education - no way we could afford private at the moment). Looking at the mums/nannies in the playground, they have minimum 2 kids, maybe 3 or 4, so no wonder the quoata is nearly filled when siblings have been allocated their place. There are two other state schools withing walking distance to my dcs school, and they have a much wider mix in ethnic belonging than my dcs school, although there are different european nationalities in his school, and many children in his class are bilingual.
I think that goes for many Faith schools, they welcome other faiths than their own in theory but in reality when looking at the entry requirements in pecking order, there is no space left for children of other faiths.