More than eight out of 10 parents want tougher laws against online pornography, a survey carried out by the London School of Economics claims.
41% of parents check up on their children's internet use
UK families seem to be more restrictive than in Europe when it comes to letting children use the internet, it found.
But researchers say fears over its misuse mean some parents are too strict on allowing access - and may be harming their children's education.
More than 1,500 youngsters aged nine to 19 and 900 parents were interviewed.
But while European children had less restrictive access to the internet, British parents are less strict than in the US, where 62% of parents check up on their children's internet use afterwards, compared with 41% in the UK.
The two-year study also found 85% of UK parents wanted to see tougher regulation of pornography and nearly one in five parents (18%) said they did not know how to help their children use the internet safely.
Sonia Livingstone, professor of social psychology at LSE, said: "Now that many young people rely on the internet for information, homework help and careers guidance, the more it matters that some of them are getting left behind.
"Not knowing how to best use the internet may have a negative impact on their education and employment opportunities."