It says companies should face heavy sanctions if they fail to remove posts within 24 hours of a complaint.
In Germany sites face fines of up to 50 million euros.
Calling for stronger regulation in an interview with the Telegraph, Bishop of Gloucester Rt Rev Rachel Treweek (pictured below) said: "I would like to see a much more robust system of reporting.
"Young people need to feel in control when they report something that upsets or harms them.
The Bishop who led a body image campaign last year also said companies should be held to account.
"There should be a way where we can fine them if they don't take a complaint seriously. We have managed to regulate electricity where there's an ombudsman. Or if you buy something in the shops, you can complain to a consumer body.
"There needs to be a way where the social media companies have to show what they have done and an ombudsman system to take action if people are not content, with some sort of fining system like Germany's.
The comments come just weeks before the Culture Secretary produces a report into online harm.
Although most social media sites have ways for users to highlight damaging content, the companies who run them aren't currently bound by any regulations.
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