Breadandbutterfly - what I find unfair (as illustrated in the example I gave above) is that people with a faith have equal rights to community schools, and the added option of getting priority for a faith school if there is one in their area, but people without a faith have no corresponding priority for places at a community school, but can end up getting landed with a church school against their wishes.
This may not happen much at secondary level, as there are not as many faith-based secondary schools, but it certainly happens a lot at primary level. In some areas, more than half of primary schools are church-linked.
Eg, where I live now, I am almost exactly half-way between a Catholic primary and a community primary - both oversubscribed. If I were Catholic my children would definitely get a place at the Catholic primary, as the catchment area is wider for practising Catholics. And in my current house, I would almost certainly get a place at the community school.
However - if I had unwittingly bought a house a couple of streets further towards the Catholic school I would, if I had a reception aged child this year, probably be in one of the admissions black holes where I am too far from any of the nearest community (or voluntary-controlled CofE) schools to get a place, but would not be entitled to a place at my closest school (the Catholic one) because of my lack of religion. I would then be thrown into the situation of being given a place at an undesirable school miles away on the other side of the city, if I got any place at all (in recent years some families in my city have ended up with no school place at all).
It is not always possible to plan these things by buying/renting a house in the right place, even if your personal circumstances allow you a choice, because the effective catchment areas of schools expand and contract depending on the number of children of a certain age in any given year. A few years ago the catchment area for most of my local schools would have been over 1km; now it is often less than 300m.
And fwiw, atheists actually have no options at all for non-religious schools - all schools in the UK are meant to be religious to some degree (daily acts of worship of a broadly Christian nature etc etc). And as breadandbutterfly pointed out, people of minority religions also have no option of a state school which promotes their own beliefs.
I really don't see why religion has to be part of the state school system at all - much fairer if all state schools were non-religious and suitable for everyone, with families taking care of indoctrination in their own religious faith at home or at their place of worship, or paying for a private religious school (as happens in other countries, like the US and France).