Research by the online discounts website revealed that 48 percent of those parents have no idea what their children get up to on social networks.
Furthermore a quarter of parents said they believed their children would keep themselves safe online.
MyVoucherCodes also said that a third of parents had no idea what privacy settings were in place on their child's social network profile.
Of the 22 percent of parents that didn't allow their children to use social networks, only 25 percent said it was because they believed it may be unsafe, while half said it was because they believed a social network to be detrimental to their child's education.
Facebook was voted the most popular, with 79 percent of social networkers under 15 years old admitting to having a profile on the site. It was closely followed by Bebo and MSN.
One in ten parents also admitted they had let their child lie about their age to join Facebook, as the site's minimum age requirement is 13.
Mark Pearson, MD of MyVoucherCodes, said: "I think that it is very important for children to be able to use these sites to an extent because it is a great way for them to keep in contact with their friends.
"I do think however, that the access does need to be limited because over exposure can be bad for their health. Also, it is vital that children are monitored and privacy settings are kept in check to ensure no personal information is accessible to strangers."