The firms would have to appoint named executives who would be personally liable for ensuring their duty of care was upheld.
The NSPCC is also concerned that ministers are preparing to scale back action against “legal but harmful” behaviours such as cyber-bullying, self-harm and sexting.
However, Mr Wanless said the Government needed to take a tough line to prevent a repeat of tragedies like the death of Molly Russell, the teenager who took her life after viewing self-harm content on Instagram.
He said the tech giants offered “heartfelt responses” to such individual tragedies, but then got “distracted” and “moved on” when what was needed as a law that would “concentrate their minds” force them to design duty of care into their platforms.
He said the firms lacked a “deep enough knowledge” of the predatory and abusive behaviour of online paedophiles and were not prioritising it enough.
“I don’t think people are wilfully encouraging this stuff to happen but they are allowing it to happen,” said Mr Wanless. “Sitting where I am, it’s a misplaced sense of priorities.”
He highlighted figures which showed there was a 60 per cent rise in calls to the NSPCC helpline about online sexual abuse during lockdown, from 117 a month to 187, and an 11 per cent rise in Childline counselling sessions about online sexual abuse from 207 to 230 a month.
The NSPCC also want an independent regulator with powers to force firms to hand over any data it needed for investigations, publish annual “transparency” reports that gave a full list of incidents putting children’s safety at risk and to require improvements such as tougher age checks.
Mr Wanless said: “The Covid pandemic has illustrated the devastating consequences for children of not having a duty of care online. The pandemic is the new context but it is not the underlying reason.
“The underlying reason is the failure of these companies to face up to their duty of care obligations for far too long. Now is the moment.”