My dd 8.5 has always been an abysmal eater. she seems to have not appetite whatsoever. I send her to school with a small roll, some salami sticks, a bunch of grapes and a biscuit and a carton of juice. She generally has a weetabix, some flakes or a slice of toast for breakfast and that is a struggle to get down her. When she comes out of school she inevitably has the sandwich and grapes but won't eat either and gets stroppy when I won't give her chocolate. I don't think she gets enough time to eat her lunch and is too busy chatting with classmates. The school don't seem to supervise very closely either despite me asking her teacher to watch her. We did have issues where another girl was taking her snack, this has pretty much stopped but still she doesn't eat. so in a word, nothing to offer except sympathy.
Out of my DD twins (9) I have one good eater and one not so good. She rarely eats much for breakfast and it drives me nuts too. They have school dinners but as there is no choice at school they only eat if they like it, otherwise they just eat bread and fruit for lunch.
I try to vary breakfast as much as possible with different cereals or toast or eggs (if we have time). Would she eat a couple of digestive biscuits and some fruit - I remember hearing a doctor once saying that that was a fairly nutritious breakfast if you were in a hurry.