My ds's school is the same. They use 1 particular church (it is next door). Also, once a term the reverend from that church takes assembly. And, once a term they get the SCAT team in for assembly. (Schools Christiam Assembly Teaching ?) So for a non-denominational school there is an awful lot of churchy things going on!
I am happy to go along with it for now, but I do answer dd's comments of 'God made the world' with 'well, that is what some people believe' because I refuse to let her be brainwashed at such a young age. (The school is an infant school, so the dc are aged 4 - 7 and thus so very impressionable)
Ds is at the local junior school and that is also non-denominational. But they say a hymn in the daily assembly and do a prayer too. Luckily ds (now just 8) is more open-minded about it all and is questioning different religions with interest. At the moment he wants to be a bhuddist.