I think it would mainly be parents dropping off and picking up at the back entrance to the school.Having a school nearby does come with some problems. The school bus stops right in front of my house and the kids make a mess out there, dropping candy wrappers and juice boxes, paper trash, etc. I swear parents these days are raising a generation of litterers!
It wouldn't necessarily bother me though, because I would have left earlier and come back later from my school and they would have the same holidays as me , but it could put off some buyers. The Sunday car boot sales may cause a problem but, as you said, I need to ask the neighbours if they do.
I think they should fine parents if their kids are caught dropping litter. You could also try ringing the school and let them talk to the kids about respect for neighbourhoods - no need to give your address.