This kind of bullying can be as bad as any other, campaigners say
Cyberbullying is a growing problem in primary schools, according to the Anti-Bullying Alliance.
In a small study carried out by the group in south east England, one in five children questioned said they had been bullied online or by phone.
And many of the 227 10 and 11-year olds questioned said they used social networking sites, even though users are meant to be over 13.
Campaigners say parents must learn how to help children protect themselves.
In response to concerns, the social networking site, Bebo, is to introduce a button which allows users to contact child protection workers.
The button will give advice on how to deal with issues such as bullying and contact details for the police and child protection staff.
The Anti-Bullying Alliance (ABA), which is a charity bringing together 60 organisations, released the findings of a survey of parents on cyberbullying at the start of 'Anti-bullying week'.
It defines cyberbullying as deliberately upsetting someone using information technology, especially the internet or telephone.
The survey suggests 89% of parents thought cyberbullying was just as serious as other types of bullying.
About half (54%) of those questioned said they had not talked to their children about how to protect themselves from cyberbullying.
Almost a quarter (23%) said they would allow their child of 10 or under to go on the internet unsupervised at home; 38% said they had or would allow children of that age to have a mobile phone.
And one in 10 of the parents surveyed said they had or would allow their child of eight or under to have a mobile phone.
The research involved 1,163 people in England who have children aged between eight and 14. It was conducted by BMRB in October 2009.
The chairman of the ABA , Christopher Cloke, said: "Parents and schools need to be aware that cyberbullying is affecting younger age groups as more children get mobile phones and have computer access.
"Nationally we know that around 22% of secondary school pupils have suffered cyberbullying, but until now we did not know younger age groups were also seriously affected.
"It is crucial that we ensure they know how to stay safe online, and that their parents know how to help them. Clearly more research is needed on this emerging issue."
The group believes some people do not take this form of bullying seriously because it is indirect and often anonymous, but they say it can be harmful, leaving children feeling that they cannot escape.
One child told campaigners: "I felt that no one understood what I was going through. I didn't know who was sending me these messages.
"I felt powerless and didn't know what to do."
The group tells children:
• Don't give out personal details such as your mobile number, address or email online
• Regularly check and clean your friends lists on social networking sites
• Keep evidence - callers and mailers can be traced
• Find the "report abuse" or "block sender" options on your favourite websites
• Remember that sites you create and emails you send can be traced back to you
• Protect your password to keep your files and information safe
• If you are being bullied in any way you must tell someone who can help - a teacher, parent/carer, friend, sister/brother or other relative