Half of children surveyed say they spend too much time online.
Almost a quarter have admitted they saw something online in the past year that they wouldn't want their parents to know about.
The study of 1,600 8-12 year olds is being released to mark Safer Internet Day.
It also found that 30% of children can go online whenever they want, a quarter said they were not allowed online before bedtime, and 3% of children said they are never allowed to go online.
It found 43% said they were not allowed to chat or game with strangers, over half said they were not allowed to add friends they do not know and almost a third said they were only allowed online at certain times.
When compared by gender, the study found that a higher percentage of boys than girls had no rules in place for going online.
A quarter of children surveyed said that they find it hard to switch off from games and apps.