The amount of time UK kids spend online is actually double parents' estimates, according to Symantec.
The Norton Online Living report, which is conducted by the security firm every year, revealed that kids are spending on average of 43.5 hours per month online surfing the web, compared to the 18.8 hours their parents think. A further 31 percent of kids also claimed their parents didn't know what they looked at online.
However, one in five parents said they had caught their kids looking at inappropriate content online and 54 percent had installed parental control software.
Three quarters of parents said they have discussed safe online practices with their children while 65 percent also felt they were extremely knowledgeable when it came to discussing whether to share personal information on the internet with their children.
"Having an open discussion with your children is something we really encourage," said Marian Merritt, Symantec's internet safety advocate.
"It's not about coming down hard on them when they encounter inappropriate content, as the internet is a great place to learn and to play, but there have to be boundaries. Kids in the UK are pretty internet savvy, and parents need to keep up."
Mo Shapiro, Relationship Psychologist, added: "We are naive if we believe that parents will always know exactly where their children are online or anywhere else. They need ground rules to help them understand what is and isn't safe".
"What's encouraging about these results is that open discussions are taking place and maintained on the topic, and children know that they can turn to mum and dad for advice and guidance about online behaviour."
Symantec also said the internet has been good for family relationships. A third of kids have admitted to being friends with their parents on social networking site Facebook, which Symantec says indicated the internet generation gap is closing.
67 percent of adult web users also revealed the internet made keeping in touch easier and a further 58 percent said it had improved offline relationships. Symantec dubbed these web users 'e-families'.
"This group of people have struck a healthy balance between online and real-world family interaction, and have turned technology into a family asset," added Merritt.