Parents are still oblivious to their children’s internet activities despite claiming to know exactly what their children get up to online, a report has found.

The State of Internet Security report, by security software provider Webroot also shows that children are putting their parents under great risk by lying to them about their online habits.

In a survey of 600 children aged between five and 17, and their parents, the survey found that nearly two-thirds of children spent more than three hours a day surfing the web, despite three-quarters of their parents claiming that their children spent only two hours or less.

Nearly half of the children also said they used instant messaging and social networking websites  everyday. Of this number, half of those aged between 11 and 17 had received an invitation via such sites to meet someone they did not know and over a third said they had received a sexually explicit email within the previous 12 months.

However, only a third of parents said they knew their children even accessed such sites.

Despite three-quarters of their parents claiming their children never bought anything over the internet, more than half of children admitted to buying online. Only eight per cent of parents said they knew their children had downloaded music despite a fifth of children admitting to doing this.

Peter Watkins, chief executive of Webroot, said the gap in knowledge could not only lead to safety issues amongst children but also lead to some serious privacy and purchasing issues for parents.

“It’s important that parents realise their responsibility if their child engages in hacking, bullying or trademark or copyright violations committed by their children when illegally downloading music or videos. A little awareness can be very helpful,” he said.

John Carr, internet safety consultant for children's charity NCH, said Mr Watkins warning was “very true”.

“This survey reminds us that there is still a huge gap that needs to be addressed,” he told Computeractive. “Children are fearless and parents are clueless and we need to improve on this.”

To do this Mr Carr said parents should apply the same vigilance to the online world as they would in offline circumstances. He also advised parents to speak to their children about online issues and the dangers that they faced.