Many parents lack the skills to help their child's internet use, a London School of Economics study has said.
It said 85% of parents surveyed wanted stronger laws to clamp down on internet pornography.
And one in five said they did not know how to help their children use the web safely, according to the UK Children Go Online report.
In a two-year project researchers asked 1,511 nine to 19-year-olds and 906 of their parents about their internet use.
Of the young people, 98% said they had access to the internet, be that at home, school or somewhere else. Nearly one in five had internet access in their bedrooms. About a quarter relied on school.
A lack of internet skills among many parents could harm their children's prospects, the report said.
Mostly middle class, internet-literate parents raised internet-literate children, it found.
Sonia Livingstone, social psychology professor at LSE, said many now relied on the web for information, help with homework and careers guidance, so it mattered more if they were left behind.
"Not knowing how to best use the internet may have a negative impact on their education and employment opportunities," she said.
It also identified a group of "disengaged youth", unlikely to engage with the net, who did not have access at home.
Parents who restrict web use too much may make their children less aware of online risks, such as those from chatrooms, the report said.
It called for literacy initiatives aimed at parents to help bridge the divide as well as an increase in going online together.
The study called for government and industry action.
Among the parents, 86% said they did not let their children give out personal information on the internet, compared with a study that found just half of European parents asked did the same.
However, in the US, almost two-thirds of parents check their children's internet use afterwards, compared with 41% in the UK.