The poll found that 35 per cent of parents believed their child had been picked on at school and nearly a quarter said their children had been bullied physically.
The finding follows a string of bullying-related suicides by pupils.
The latest victim may have been Laura Rhodes, aged 13, who died at home in South Wales last weekend in a suicide pact with a friend. The teenager's parents said that bullying had been a factor in her death as she had been driven out of her school by bullies who teased her about her weight.
Encouragingly, three out of five of parents whose children had been victimised said they felt the school had dealt with the problem effectively. But fewer than half the parents from London said they felt the issue had been properly tackled.
Boys were slightly more likely to have suffered than girls.
Parents were also more likely to say their children were bullied if they were attending secondary rather than primary school, although this might simply be because their children were older and had more opportunities to be targeted.
The Government wants schools to have "zero tolerance" of bullying and is urging all heads to sign anti-bullying charters.