Nicky Morgan, the Education Secretary, has published a consultation looking at closing loopholes to ensure schools and colleges are keeping pupils safe when they use the internet.
Parents have also been offered a handbook on social media detailing "conversation prompts" for how to bring up the topic of cyberbullying and other online dangers with their children.
The advice urges mothers and fathers to make sure geo-location is disabled on their children's phone apps and explain that apparent online friends may be hiding their true identities.
The new drive comes amid fears that there are gaps in schools' current approach to protecting children from threats online. In particular there are concerns children are increasingly being targeted by Islamist extremists.
Mrs Morgan said: “As a parent I’ve seen just what an important role the internet can play in children’s education. But it can also bring risks, which is why we must do everything we can to help children stay safe online – at school and at home. This includes ensuring young people know how to use the internet responsibly and that parents and teachers have the right measures in place to keep children safe from exploitation or radicalisation. These measures are delivering on the government’s commitment to keep children safe from harm, as well as providing helpful support and information for professionals and parents so we are all equipped to help protect children in this digital age.”
The consultation published by the Education Department outlines a range of possible measures ministers could take to improve online safety for youngsters and will run until 16 February.
Currently, the department’s statutory guidance says that schools in England only need to “consider” teaching pupils about safeguarding online. Ministers want to change this so the teaching is “required”.
Another proposal is to make schools put internet filters on all computers and create a system of monitoring which will ensure inappropriate online content cannot be seen by pupils.