The warning was issued by the Nantwich Education Partnership in Cheshire – which represents 15 primary schools - after it found that some children had been playing or watching games that contain unsuitable levels of violence and sexual content.
Headteachers wrote to parents saying that playing such games or accessing certain social media sites such as Facebook and WhatsApp could lead to 'early sexualised behaviour' and leave children 'vulnerable to grooming for sexual exploitation or extreme violence'.
They continued: "If your child is allowed to have inappropriate access to any game or associated product that is designated 18 plus, we are advised to contact the police and children's social care as this is deemed neglectful."
Mary Hennessy Jones, the head who drafted the letter, said: "We are trying to help parents to keep their children as safe as possible in this digital era. It is so easy for children to end up in the wrong place and parents find it helpful to have very clear guidelines."
But parents' groups said reporting families for allowing children to play unsuitable computer games was a step too far.
Margaret Morrissey, from Parents Outloud, said: "Accepting the huge concerns about these violent games and their effect on children, I think the schools are stepping outside the realm of what is probably acceptable.
Elaine Halligan, director of Parent Practice, which offers training for parents, said: "Lots of adults think coercion is the key, and we absolutely don't agree with that.
"We think it's all about communication, connection and trust. What this warning does is break down trust, not only between parent and child, but also parent and teacher."
She said games such as Call of Duty had 15-rated versions that 'are cleverly created to fill the gap and suck young people into the franchise'.
She added: "I absolutely get why they are doing it – it's because children do need to be protected from technology.
"But to get the social services involved is an absolute disaster, because it starts telling parents that we don't trust you to be responsible for your children."
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