Filters put in place by parents to stop children viewing inappropriate content are easily bypassed by the youngsters themselves, according to a report from regulator Ofcom.
It found that 18% of 12-15-year-olds know how to disable internet filters.
Almost half of children aged 12-15 know how to delete their browsing history and 29% can amend settings to mask their browser activity.
Some 83% of eight to 11 year-olds said they knew how to stay safe online.
In response to the report, Culture Secretary Maria Miller said that filters were not "a silver bullet".
"Parents have a central role to play in protecting their children, including by talking to them about how to stay safe online," she said.
According to the report, many parents feel their computing skills are far inferior to their children's.
Almost half (44%) of parents with children aged between eight and 11 say their child knows more about the internet than they do. That rises to 63% for parents of 12-15-year-olds.
The government has put pressure on UK ISPs to introduce network-level filters that screen out pornography and other content deemed inappropriate.
But the filters have proved controversial.
Sky's system hit the headlines when it emerged that it was blocking a legitimate news website that covered file-sharing issues.
Meanwhile a BBC investigation found that filters were blocking out sex education websites.
Sebastien Lahtinen, co-founder of internet news site ThinkBroadband, told the BBC that the filters were easy to bypass.
"As soon as I type the filter name into Google it suggests the search term 'bypass'. The second result is a YouTube video of what sounds like a kid explaining how to work around it," he said.
"The report acknowledges that children often know more about the internet than their parents, and it is therefore no surprise that many children are able to bypass technical limitations put in place to restrict their access or delete their browsing history," he added.
"This only re-emphasises the need for active parenting and regular communications about how children use the internet, particularly at the age where they start doing so away from parents and on their own devices."