An NSPCC YouGov survey found that 95 per cent of respondents in Scotland want social networks and messaging services to be designed to be safe for children.
Some 91 per cent also want firms to have a legal responsibility to detect child abuse, such as grooming, taking place on their sites.
And 79 per cent support prosecuting senior social media managers if their companies consistently fail to protect children from abuse online.
Sir Peter Wanless, NSPCC chief executive, is urging UK Culture Secretary Oliver Dowden to listen to parents, by ensuring his landmark Online Safety Bill convincingly tackles online child abuse and puts the onus on firms to prevent harm.
Peter said: “The polling shows the clear public consensus for stronger legislation that hardwires child protection into how tech firms design their platforms.
“Mr Dowden will be judged on whether he takes decisions in the public interest and acts firmly on the side of children with legislation ambitious enough to protect them from avoidable harm.
“For too long children have been an afterthought for Big Tech but the Online Safety Bill can deliver a culture change by resetting industry standards and giving Ofcom the power to hold firms accountable.”
The NSPCC is calling for legislation to be more robust so it can successfully combat online child abuse at an early stage and before it spreads across platforms.
The charity wants a requirement for tech firms to treat content that facilitates sexual abuse with the same severity as material that meets the criminal threshold.
This means clamping down on “digital breadcrumbs” dropped by abusers to guide others towards illegal material, sadly widely available on social media platforms.
The NSPCC has been the leading voice for social media regulation, setting out detailed proposals for a Bill in 2019.
The UK Government’s White Paper consultation response in December set out the framework for an Online Safety Bill that is expected this spring.