I was the Head Teacher at Godmanchester Primary School (the largest in Cambs for most of my 18 years as head) until I retired 12 years ago. It was situated on the boundary of St Mary's School and as such had been heavily influenced by the vicars, etc.
Throughout my time at the school I took weekly assemblies for all 640 children (either in KS1 KS2 separate or once a week all together). Although I allowed teachers to take CW if they wished (which was very rare, usually at Christmas, occasionally Easter) I never once did so.
I can assure you that it was quite challenging as a head to not do CW but I stuck to my guns. Two years after I started as Head they had consultations about adding 8 additional classrooms and to respond to proposals for it to become Church aided. At the cons I spoke and said I would leave if it did so. Fortunately it stayed as it was.
The point I am making is that people wishing to opt their children out should do so as a right. Most parents, like my own daughter, who lives three doors away from my wife and I, don't bother, believing it to be harmless. I was quite cross a month ago when my granddaughter came home and said there was a man who died and came alive again. My grandson, some years before told us that a man had died in Church, that day.
I have many anecdotes from my time in school relating to the topic but I wont bore you further.
If they are not adequately provided while out of CW I suggest your daughter has with her a book to read, she will get far more from it.
Is she primary or secondary? If secondary any Dawkins, Hitchins books will do or even better check up the wonderful books by Anne Besant or Robert Ingersoll (superb 19th century atheist writers)