If you don't want children to go to school hungry, it's free school breakfasts you should be arguing for... ;-)
Surely then they would still be "Going to school hungry" unless they had a breakfast at home first.

As I understood it, school dinners (during term time) were to keep the children going through the afternoon without needing to go home for lunch. This makes the job easier for teachers (by reducing the to and fro, and avoiding a need to increase the length of the school day) and allows for 'free school meals' for those who can't afford them. But it is a simple start to a 'nanny state'. The responsibility for feeding the children should rest with the parent(s). Are those suggesting 'free' school meals during holidays planning to reduce child benefit/universal credit accordingly? Probably not.