Research suggests that while computer-mad pupils were once considered boring by their peers, they are now thought of as "friendly and fun".
The NOP poll also indicates that four million children aged between seven and 16 in the UK now use the internet.
Researchers say this represents 57% of all children in that age group, and is double the number of those who used it 18 months ago.
E-mail usage
The findings suggest that slightly more boys than girls use the internet - 53% compared to 47%.
They also indicate that 68% of pupils in secondary schools and 46% of pupils in primary schools are now online.
The researchers conducted face-to-face interviews with 1,013 children.
Further in-depth interviews were carried out with children in small focus groups, who were also observed using the internet.
Of the children surveyed, more than half said they regularly used the internet to send and receive e-mails.
Almost two thirds surf the net when they log on, while the rest go straight to their favourite site.
The survey indicates that the amount of time children spend using the internet still lags far behind the time they spend watching television.
It suggests that pupils spend an average of 1.7 hours a week logged on at home. Those with internet access at school spend a further hour a week using it.
This compares with an average 21.3 hours a week spent watching television.
Porn sites
Barbie Clark, director of the NOP Family group, which carried out the survey, said children knew more about the internet than their "technologically-challenged" parents and teachers.
"The expert in the family is, typically, a boy aged 14-16, and he knows all there is to know," she said.
"Once thought of as a geek by his peers, he is now the really cool kid in the class and will teach parents, siblings and teachers."
Ms Clark said there was a downside to pupils' extensive internet knowledge - such as accessing pornography sites.