Parents who fail the checks could also find themselves receiving attention from child protection social workers.

If accepted by ministers, the Ofsted rules would be the first state attempt to investigate and vet ordinary parents over the way they bring up their own children.

The proposal brought fierce protests from family campaigners.

Norman Wells of the Family Education Trust said: ‘It is sheer madness for Ofsted to suggest that parents should be required to undergo CRB checks to be with their children between the hours of 9am and 3pm from Monday to Friday during term-time.

‘If it is deemed unsafe for children to be with their parents during normal school hours, it is equally unsafe for them to be with their parents in the evenings, at weekends and during the school holidays.

‘If Ofsted are calling for CRB checks for home-educating parents now, how long will it be before they are demanding that all parents are CRB-checked?’

Robert Whelan of the Civitas think-tank said: ‘You can no longer be a parent without a piece of paper from the state. This is a monstrous idea and it shows the danger of taking things to logical extremes.’

A Bill from Children’s Secretary Ed Balls already backs the idea of a home-schooling registration scheme where parents must set out a curriculum and allow town hall officials to inspect their homes.

But in a written report to MPs on the Children, Schools and Families Select Committee, Ofsted said: ‘Registration would not of itself prevent those who have a conviction for offences against children, including parents, step-parents or privately employed home tutors, from home educating children.

‘Criminal Records Bureau checks should be a requirement of registration.’

The right of parents to educate their children at home has been enshrined in law since 1944.

Parents have until now not had to register with councils or tell them what they are teaching.