Not all schools have kitchens, so those schools will give their pupils sandwiches, so kids won't necessarily have a hot meal. They'll have some food, so perhaps this will help a few families, but not likely to be great for everyone.
People who are on the basic amount of jobless benefits don't get Child Benefit anyway. Or if they don't know their way around the social security system and claim it anyway, it will be taken off their other benefit.
In the schools that do have kitchens, I'm not sure there is a social stigma. No one will know who is getting their meals for free, most of the time. In my school, (years ago now), the only time we knew who was getting free meals was when we were on a field trip and grim-looking boxes were handed out to those children.