Members of the public are legally entitled to enter school grounds where there is a public right of way, which can cross playing fields, playgrounds, and even go between school buildings.
Education minister Ivan Lewis was due to announce today that heads will be able to make local highways authorities ban the public from their land.
Schools have complained that public access has resulted in vandalism and antisocial behaviour.
Mr Lewis said: "It is a totally unacceptable situation that headteachers are not able to control who comes onto their school grounds and today we are sending out a clear message that we won't allow this to continue.
"Pupils and teachers have an absolute right to feel safe and secure and that is not possible when loutish behaviour is allowed to go on.
"We are determined to tackle anti-social behaviour both in and outside the school gates and these measures will go a long way to putting power back in the hands of headteachers."
Parents and other members of the public who enter school buildings without permission can already be accused of trespassing and asked to leave.
Trespassing is not a criminal offence in itself and can only be pursued through the civil courts. However, if a trespasser refuses to leave, or is abusive, it can lead to a criminal conviction.
Ray Lockey, head of Lockleaze school in Bristol, said: "The biggest problems is with the dog walkers. They leave dog mess all round the playing fields."