Social media firms such as Facebook and Snapchat who fail to take action against the “alarming rise” in online bullying could face heavy fines and blocks on their service, a minister has warned.

The culture secretary Jeremy Wright also said that members of their senior management teams could be held individually liable.

Mr Wright said he wanted social media operators to make it easier for victims of online bullying to report it so that swift action could be taken to remove posts and “stop bullying at the source”.

He told the Sunday Times that he had been bullied at school, but was able to leave it behind at the end of the day, whereas nowadays “young people carry it with them on their smartphones, so it can be with them 24/7”.

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The son of teachers, Mr Wright, who was educated at the fee-paying Taunton School in Somerset and Trinity School, New York, said his friends were also bullied at school.

In a statement ahead of his appearance at an anti-bullying event hosted by Facebook tomorrow, he told Tes the government was set to appoint a regulator with the power to enforce tough sanctions.

He said: “While some social media platforms have made progress in tackling the alarming rise of cyberbullying, it’s not happening fast enough. There’s a lot more that needs to be done to better protect children online.

“Platforms also need to be much more vocal in their condemnation of this kind of victimisation and bullying, be crystal clear to offenders about the steps they will take if this behaviour is identified, and much quicker in responding when incidents of bullying are reported to them.”

“The regulator we appoint will have a range of enforcement powers to take action against companies that fail to fulfil their duty of care. We are considering granting the regulator the power to issue substantial fines, imposing liability on individual members of senior management, and the authority to block non-compliant services.”

Figures from the Anti-Bullying Alliance (ABA) show a third of 11- to 16-year-olds have been bullied online, at least once in the last six months.

And new figures are to be published tomorrow at the Facebook event which will showcase the work of students and schools who have adopted the anti-bullying ambassador programme created by The Diana Award charity, which is supported by Princes William and Harry.