One in five parents has a child who has been bullied in the past year, according to a survey.
Parents' responses to one of the questions
The poll of 1,600 parents, for the umbrella group of England's parent-teacher associations (NCPTA), suggests bullying is an important issue for 97%.
At the start of the first national anti-bullying week, campaigners said most parents believed more should be done to tackle the problem.
More than 50 organisations are involved in a drive to reduce bullying.
Olympic gold medallist Kelly Holmes and
England defender Rio Ferdinand have made a video supporting the campaign.
Of the 21% of parents who said their child had been bullied in the past 12 months, six out of 10 said the bullying had been verbal. Three out of 10 said it had been physical.
Nearly 80% of bullying incidents reported took place during break or lunch periods and the playground was the most common place for a child to be bullied, the survey found.
David Butler, NCPTA's chief executive, said the work of the government and groups such as Childline and the Anti-Bullying Alliance had helped to reduce bullying, but more action was needed.
"Much more needs to be done to stop the misery and heartache bullying causes to the victims and their families," he said.
"Children that are bullied at school miss out on valuable learning opportunities and are prevented from reaching their full potential."
"Parents understandably want to feel reassured that everything is being done to keep their children safe at school," said Alison O'Brien, chair of the Anti-Bullying Alliance and education advisor for NSPCC.
"For their part, teachers want to tackle bullying effectively but they sometimes need back-up in dealing with such a complex issue."
'Yob in every playground'
She added: "We hope that Anti-Bullying Week will kick-start activity in schools and motivate those working with children to look at methods which are proven to be successful.
"Our team of regional coordinators will be working with schools and LEAs to provide extra training and support."
The shadow education secretary, Tim Collins, said: "While we fully support this campaign to stamp out bullying, ministers' recent policy announcements have made this a far more difficult goal to achieve."
Charles Clarke's determination to require every school to take in poorly behaved pupils means that Labour are guaranteeing a yob in every playground and a thug in every classroom."
The charity Mencap said the need for help to tackle bullying was even more urgent for children with learning disabilities, who were seen as "easy targets" by bullies.