A Sky Data poll has revealed that 91% believe social media makes bullying worse - with the mother of one victim describing some of the survey's results as worrying.
More than 1,000 people were surveyed for the research, and just 1% of respondents believe that platforms such as Facebook, Snapchat and Instagram make bullying less of a problem among children.
Almost two in three of those polled - 64% - think smartphones should be banned from schools.
But despite this, 56% believe that teenagers should not be banned from social media, with 27% saying they would be in favour of such a proposal.
Lucy Alexander's 17-year-old son Felix killed himself in 2016 after suffering years of online abuse.
Since his death, she has been campaigning to make social media a safer platform. However, she told Sky News that an outright ban on children using these sites would be counterproductive.
Ms Alexander said: "If you take away social media from children you will isolate them further. Like it or not, that's how they communicate.
"So we need to teach them from a young age that social media should be a tool, it shouldn't be their life.
"And to do that we need the government, teachers, parents and social media companies to work together and create a joined up approach to the problem."
The poll comes as the Royal Society for Public Health (RSPH) urges people to give up social media for the whole of September, or cut down on how much they use these sites.
Its campaign, Scroll Free September, comes amid growing concern about the impact of social media on mental health.
A RSPH survey revealed that two in three social media users would consider getting involved in the initiative, with most participants believing that logging off these platforms would have a positive impact on their lives.
Many of those polled said going cold turkey would benefit their sleep pattern, enhance their real-world relationships, aid their mental health and improve their body confidence.
Shirley Cramer, the society's chief executive, said: "The aim is that, by the end of the month, we will be able to reflect back on what we missed, what we didn't, and what we got to enjoy instead of scrolling through our news feeds.
"That knowledge could help us build a healthier, more balanced relationship with social media in the future.
"Of course, we know this will be a challenge because of the addictive nature of social media technology, which is why we need to work closely with the government and the social media industry to create an online environment that is more conducive to positive mental health and wellbeing."
Sky Data interviewed a nationally representative sample of 1,006 Sky customers by SMS on 6 July 2018. Data are weighted to the profile of the population.
For full Sky Data tables please click here.
:: Anyone feeling emotionally distressed or suicidal can call the Samaritans for help on 116 123 or email email@example.com in the UK.