Internet Matters, who conducted the survey, also found more than forty percent of parents don't supervise their children's internet use in anyway, and nearly a third didn't know how to install filters on their children's devices.
It comes as Prime Minister David Cameron's announced a new law is being brought in, which means paedophiles who ask for sexual images of children online could be imprisoned for two years.
David Cameron also announced the National Crime Agency, together with intelligence agency GCHQ, would be setting up a unit to tackle the encrypted network, known as the "dark web", where images can be exchanged in secret on the internet.
Carolyn Bunting, from Internet Matters, told Premier: "Without parental controls in place, children can access content that's inappropriate like pornography, like violence, like crime... which I don't think parents would want their children to see.
"Parents are really confused, and their perception around parental controls is that they're complex and time consuming and difficult to set up. What we wanted to do... is tell parents that it's not that difficult.
"Where parents are using parental controls, the satisfaction with them is really really high. Once they've understood parental controls and they've set them up, the overwhelming majority think they're a really good idea.
"Technology moves at such a pace now that it's hard for parents to keep up, and I think they feel that their children know more about the internet than they do, and therefore they're not best placed to advise their children.
"We would encourage parents wherever possible to talk to their children, get their children to show them what they're doing online, get their children to teach them about what they're doing online.
"That way you're just in a much stronger position to guide your children through their lives on the internet.
"Combined with using the tools that are in place I think that will keep children as safe as we can."
The three biggest worries expressed by parents in the survey were "stranger danger" (21%), that their children may experience bullying (19%), and that their children may see inappropriate content (18%).
Simon Bass, Churches Child Protection Advisory Service:
