If the building she's in is their property, then they very likely do have that right. (I'm not condoning their decision, of course.)
Of course, paying for council run schools is compulsory.
You're right, but what I was trying to say was
"A school is ... compulsory for all children" (home schooling being special case of school).
You may well be right. Still, I find the concept questionable. I mean forbidding the lawful use of her property (camera, lunch), just because she is inside someone else's property? She is not photographing the school.
Besides, council property does not belong to the council officials but to the residents in the area and I suspect that, if their rights and opinions were respected, this order would not have been issued.
"In general under the law of the United Kingdom one cannot prevent photography of private property from a public place, and in general the right to take photographs on private land upon which permission has been obtained is similarly unrestricted. However landowners are permitted to impose any conditions they wish upon entry to a property, such as forbidding or restricting photography."
I think the council would argue that they are enforcing the ban of photography to protect the children from people who might want photographs of the children. I know when I used to work with children we had to get written consents from parents before any child could apear in a photo and in some cases we were instructed to make sure some children were never photographed and step in the way if we saw anyone with a camera.
That said letting the kids loose with cameras is going to be quite disruptive.
When you think of it from an adult perspective, the idea that an arbitrarily-chosen authority figure can walk into the room, tell you to put your hands on your head for no reason, and if you don't put your hands on your head then you get punished, is pretty weird. But children have fewer rights than adults and there's no good way around that except to suck it up and wait a few years.