They are spending so much time online that one in three now struggles with offline activities that require concentration such as reading a book, according to the report.
While three quarters believe their child spends less than an hour a day online, children admit that they are actually surfing the web for an average of two hours a day.
Although two thirds said they had had a negative experience online, only 22 per cent of parents realized this.
Dr Aric Sigman, a leading psychologist, said: “The problem with this generation is that we accept there should be limits on the consumption of many things, such as sunlight or sugar and salt, but screen time is not something that is thought of as consumption.
“It is important to impose boundaries, rules and limits. What parents often assume is a benign pastime is their main waking activity and the sheer amount of time that children spend at screens can lead to increased risk of physical disease as well as psychosocial issues.”
The survey, which is believed to be the first to involve both children and parents, found that one in seven under-16s are so addicted to the web that they spend four hours or more glued to the screen.
More than a third begin to feel “angry and grumpy” if they cannot get online whilst one in five expressed concerns that they spend more time in the virtual world than with real people.
While more than half said they had accidentally accessed inappropriate content online, one in 11 admitted looking for it deliberately. A quarter said they had accessed eating disorder sites and one in five had looked at self harming websites. More than one in ten admitted viewing suicide sites and child abuse images.
Almost one in five admitted that had “thought about” trying what they had seen online but 98 per cent of parents who knew their children had accessed inappropriate material had no idea they had been influenced by it.
One in 20 revealed that they had met up with a stranger they first met on the internet.
The rapid rise in the use of smart phones and computer tablets means that banning screen time has become the modern equivalent of “grounding” children, with three quarters of parents imposing limits on internet use.
However, one in eight children disclosed that they continued to access the web in secret or pestered their parents until they gave in and reversed the ban.
Almost 30 per cent of parents allow their children to access the internet without any restrictions or supervision, with one in eight letting toddlers aged two or under go online. Just one in seven wait until their child is at least ten before allowing them access to the internet.
Despite the findings, the report suggests that children are aware they are spending too much time online, with almost three quarters wanting their time limited to under two hours.
Overall, most parents remain heavily in favor of web use with over half supporting it for homework and 82 per cent stating that their child had developed “great computer skills” which will help their future job prospects.
More than a third said the web meant their children knew far more about they world than they did at the same age.
Siobhan Freegard, co-founder of Netmums, which questioned 825 children aged seven to 16 and 1,127 parents, said: "The web is an amazing invention and a vital part of our kids' lives, but technology is moving so fast, that it's impossible to predict the effect it will have on our kids.
"No past generation has ever had access to so much information so fast – and not all of it desirable – along with the use of dozens of different electronic gadgets.
"Some scientists have predicted large amounts of internet exposure may alter the way kids think and in many ways we are in the middle of a giant experiment with our children as the subject. We are raising a generation of technical geniuses – but at what cost?"