The survey found that while nearly 70 percent of parents said they monitored their children's use of the Internet, only 32 percent said they used a technical filter that limited access to certain kinds of Web sites.
The survey, conducted late last year by the BBC, the Broadcasting Standards Commission (BSC) and the Independent Television Commission (ITC), concluded that the Internet as a medium raises more concerns and uncertainties than television for parents monitoring their children's media consumption.
Media publicity has made parents cautious about sites featuring pornography and paedophilia, and about chat rooms. Even when they were confident in their children's ability to regulate their own use of the Internet, they still worried about accidental exposure.
However, when it came to actually controlling their children's usage, parents did very little, according to the survey findings.
Most control, as with television, tended to be informal -- such as placing the computer where it was visible or only allowing the parent to switch on the computer. Parents in the survey felt this was the most effective way of balancing their anxieties with the educational potential of the Internet.
Out of the 32 percent of parents whose children were Internet users who said they used a technical filter of some kind (either software or ISP-based) around 62 percent of this group thought they were effective, while 11 percent thought it blocked too little.
But, most parents felt that the current technical tools available for controlling their children's use of the Internet were too complex to install and lacked simple age categorisation. They wanted simple labelling and easy to use filtering systems.
However, the propensity for "accidental exposure" meant that there was a greater urgency among many of the parents surveyed that more needed to be done to deal with the unregulated nature of the Internet.
"The whole issue of censorship and control has been left way behind by technology, because as soon as people got the Internet into the house, there was something so new and so different and potentially so dangerous for children in people's houses and I don't think either the law or protection has really caught up with that," said one parent in the survey.
Some parents were aware of informal actions such as using the history button, registering site warnings, and using top-level domain names, but few knew about more effective parental or server-based control mechanisms such as password protection or ICRA (Internet Content Ratings Association).
The study included interviews with 36 parents, carers and children from London, Solihull, Newcastle, Cardiff and Glasgow from homes with and without access to multi-channel television and the Internet. In addition, over 500 parents of children aged 5-16 took part in a survey.