The World Today: Dangers of networking; PARENT WARNING: Youngsters must be monitored.
It published research showing that 27 per cent of eight to 11-year-olds who have internet access bypass online age restrictions to put their profiles online.
The report found that many parents and children lack awareness of the issues surrounding privacy and safety on the internet.
Since they first appeared in the late 1990s, social networking sites have flourished with the launch of Friends Reunited in 2000 and more recently Bebo, MySpace, Facebook and a Saga site for over-50s.
Today Ofcom said the websites - many of which are based in the US - could do more to remind people of the risks involved in putting all their details online.
The research found that, of those with internet access, almost half (49 per cent) of eight to 17-year-olds and just over a fifth (22 per cent) of adults now have a profile on a social networking site.
But 16 per cent of parents do not know who can see their children's profiles and many believe that their children are safer online than they actually are.
While 41 per cent of children admitted that they did not use privacy settings, only 30 per cent of parents knew that their children's profiles were open to view by anyone online.
The research also found that although 65 per cent of parents claim to set rules on their child's use of social networking sites, only 53 per cent of children said their parents set such rules.