The claim comes as ministers consider curbing rights of way through schools.
PE teachers at one northern primary have been given mobile phones following frequent threats from people walking dogs.
In another case, more than 20 windows were broken in one weekend at a boys' secondary in the South. The school had installed closed-circuit TV, but the head said the vandals knew how to avoid the cameras.
And at a mixed secondary in the West Country, cars are reported to have been dumped and set alight on a school field. The school estimates it needs to spend pound;70,000 on fencing but its annual repairs budget is just pound;32,000.
The Catholic Education Service revealed these incidents to the Government, while the Church of England education board tells of a child at a south London junior school who was intimidated by a man walking his greyhounds on the path across the playground.
The Department for the Environment, Transport and the Regions has proposed restricting rights of way through schools.
Nigel Ellway, a spokesman for the Government's Countryside Agency - which advises on rural affairs - said: "We would like to see a full and accessible network of rights of way throughout the countryside, but there are exceptions where people's safety is involved.
"It might be a good idea for there not to be rights of way, for example, in school playgrounds."
Three years ago the Department for Education and Employment's working group on school security recommended councils consider changing rights of way identified by schools as a risk.
Councils and the police were concerned that criminals were using footpaths and back-alleys as escape routes.
The DETR is consulting on a paper entitled Improving Rights of Way in England and Wales.
Michael Power, of the Catholic Education Service, has already raised the issue with the school security working group and it will be discussed in September.
Daphne Griffith, education administration officer for the Church of England board of education, said: "It does worry parents when they see that people can get access to children when they think they are safe at school."
The Ramblers' Association, however, said the law already allows schools or councils to propose diversions to paths.
Spokeswoman Katey Karam said: "We have every sympathy for a school's concern for children's welfare, but we don't see the need for a change in the law."