Before organizing a whole new group, one does have to keep in mind that the play group space does not appear to be paid for, but is rather offered in generosity rather than obligation by the church involved. One can't go, "Well, we'll just meet some other time, then," if the church is not willing to let you have that space at another time.
As must as the group may not want a religious cast to the group, it would be wise to remember that without the church, they would have no free space in which to meet, and they have limited leverage here.
I think a talk with the minister would be the best way of clearing things up. Like others, I suspect that s/he is not aware of the dynamics going on here.