The crackdown was quietly given the go-ahead just before the summer recess and comes ahead of the Government's White Paper plans for a statutory duty of care to combat online harms, which will cover social media companies' and messaging apps' entire output and not just video.
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The Telegraph has campaigned for a duty of care to better protect children online since last year.
The culture department said the new powers on videos were scheduled to come into effect in September next year, subject to a consultation this summer and a statutory order in Parliament.
"These rules are an important first step," said an Ofcom spokesman. It is also a sign that Ofcom could take up a role as a "super-regulator" charged with policing the White Paper laws on online harms.
The move has been made possible by "off-the-shelf" legislation set out in an EU directive agreed by all countries including Britain. The Audio Visual Media Services directive extended regulation from TV and video-on-demand services to "video sharing" platforms.
Andy Burrows, the NSPCC's head of child safety online policy, said: "This is a real chance to bring in legislative protections ahead of the forthcoming Online Harms Bill and to finally hold sites to account if they put children at risk.
"The immediacy of livestreaming can make children more vulnerable to being coerced by abusers, who may capture the footage, share it and use it as blackmail."
An NSPCC survey of 40,000 children aged seven to 16 found a quarter had livestreamed, and one in eight had video-chatted with someone they had never met. Of those, one in 20 had been asked to remove clothes.
Simon Bailey, the National Police Chief Councils' lead on child exploitation and abuse, told The Telegraph that live-streaming had become a magnet for paedophiles, as social media platforms and apps rushed to add video to their sites.
Damian Collins, chairman of the Commons culture committee, last night said the new steps were "important interim measures," but added: "It is essential that the White Paper is implemented in its entirety so that the full extent of online harms can be tackled. I would ask that the Government reasserts its commitment to do this."
Under the new measures, Ofcom will be charged with ensuring firms comply with "minimum standards" to protect "minors" from content that incites "violence or hatred" and criminal content such as child abuse images or terrorism.
Ofcom will also get "appropriate information gathering" powers to order the firms to hand over data or algorithms, which have been blamed for driving content to vulnerable children, such as in the case of Molly Russell, 14, who committed suicide after viewing streams of self-harm images on Instagram.
Facebook has also been widely criticised for failing to take down videos of the livestreamed Christchurch mosque terrorist killings, while YouTube has come under fire for failing to take action against far-Right extremism and "drill" videos that incite gang violence.
The culture department listed eight key measures expected of video-sharing platforms including "effective" age verification systems, "transparent and user-friendly" mechanisms for users to report or flag videos and robust complaints systems.
Those breaching the rules face "maximum fines of the greater of £250,000 and five per cent of the provider's qualifying revenue, as [Ofcom] deems to be appropriate and proportionate."
"Offences also exist for failure to comply with enforcement measures, with Ofcom also having the power to suspend or restrict the entitlement to provide a service," said the culture department.
It said Ofcom would be the "interim" regulator "until such time as an online harms regulator is appointed under the Online Harms legislation".Campaigners expect a beefed-up Ofcom to take on that role.
New York-based hate content researcher Eric Feinberg said, "The United Kingdom law or proposal to fine the tech companies is a step in the right direction."
But the Global Intellectual Property Enforcement Center (GIPEC) co-founder added, "My biggest concern is who is going to check or provide oversight to make sure tech companies remove content in a timely manner
"It has been almost five months since Christchurch attack and I'm still finding raw video of the attack on these platforms."
"First social media PM"
While Ofcom plans to crackdown on social media, Facebook and its peers got a boost from Boris Johnson's pronouncement that he is planning to make more Facebook live broadcasts to the nation in a bid to become the first "social media Prime Minister" - a bid that could draw parallels with NZ Prime Minister Jacinda Ardern's high-rotate use of the social network.
Following the success of Johnson's recent 'live from my Downing Street desk' public address, Number 10 is looking at 'new innovative ways' to connect with the public - including holding online question and answer sessions dubbed 'People's PMQs.'
"That was not a one off," said a Downing Street insider. "This is recognition of the fact the public cannot get enough of the Prime Minister. He is at his best when he is meeting people so we're trialling digital ways for him to do more of that."
The online project is being pioneered in-house, using a Number 10 tech team.
Additional reporting by NZ Herald staff