Almost a quarter of 11 and 12-year-olds who use social media have been upset by something on it over the last year, a children's charity has warned.
The NSPCC found that, of these, 18% felt upset or scared for weeks or months after the online incident occurred.
The poll of more than 1,000 youngsters also found that a fifth of children who had been upset by an online incident such as trolling, bullying or being sent inappropriate sexual messages, experienced this every day or almost every day.
The NSPCC said that 11 and 12-year-olds were more likely to suffer a bad experience while using a site which is supposed to have a minimum age of 13.
The charity is calling on social networking sites to acknowledge that there are under age children using them, and commit resources to better protect them.
The sites should also ensure that users under the age of 18 automatically had the highest possible privacy levels for the profile pages, it said.
"There is a significant jump in the numbers of children who have a social networking profile at age 11 - which coincides with the move to secondary school for most UK children," Claire Lilley, NSPCC's head of child safety online, said.
"We estimate that around half of the UK's 11 and 12-year-olds have a profile on a social networking site with a minimum age of 13.
"This is putting them at risk of being exposed to content and behaviour that many of them just aren't ready to deal with.
"Age verification is a nut that social networking sites are yet to crack.
"But in the meantime, children are routinely bypassing minimum age limits to set up profiles, so it's vital that parents are made aware of the risks.
"We want social networking sites like Facebook and Twitter to take a pragmatic approach - if younger children are determined to use social networking sites for over 13 year-olds, the sites can't simply turn a blind eye.
"So we want social networking sites to focus on making their service as safe as it can be for all children and young people, so that if under 13-year-olds do join them they can get help easily.
"And as parents play a vital role in keeping children safe online, we want Ofcom to produce new information for parents in a way that makes it easy for parents to understand which sites are suitable for children of different ages."
BeatBullying founder Emma-Jane Cross added: " This research underlines the urgent need for social networking sites to take their young users' safety much more seriously.
"We believe in the right of children to go online without fear of being bullied or harassed, and this cannot be achieved until social networks put adequate resources behind safeguarding and user verification policies."