Parents whose children attack or threaten classmates could face fines of up to £1,000.
The warning by schools minister Jacquie Smith follows a surge in violent cases across the country.
Speaking at the start of anti-bullying week, she said troublemakers would "not be tolerated" and pupils would be encouraged to lobby their schools to adopt the Government's Anti-Bullying Charter for Action.
The scale of the problem locally was highlighted when a teenager was attacked last week with a bike chain outside school.
His parents, Alan and Julie Edwards, from Castlemorton, are concerned measures to tackle bullying are ineffective.
They called police after Alexander, 13, was attacked by fellow pupils at John Masefield HIgh School, in Ledbury, one armed with the chain.
Mrs Edwards does not believe enough is being done to protect her son, who has been bullied persistently for more than a year.
"They seem to get away with it, they get warned and sent home from school for a day and then allowed back," she said. "Hopefully, if they get frightened off by the police it might make them learn.
"The school claims to have a good anti-bullying policy but I'm yet to see it work.
"My son has been told there are safe places he can go, but rather than telling him to hide they should be tackling the problem."
Headteacher Andy Evans said the school's anti-bullying policy aimed to stop bullying and deal quickly and effectively with any instances that did occur.
"We take all incidents of bullying very seriously," he said. "Bullies will be punished and we would go as far as to permanently exclude persistent offenders."
He said bullying was rare at the school, but that he would ideally like to see none at all.
"I want every child to feel safe and enjoy coming to school," he said.
"Schools should give a strong message that bullying is unacceptable."
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