Families who home-school their children could come under investigation over fears the practice is used as a means of radicalisation, the government has confirmed.

The education secretary, Nicky Morgan, has reportedly decided to look into those educated by their parents after pledging to clamp down on madrasas teaching antisemitic beliefs.

Exact figures for the number of children who are home-schooled are unknown but the Independent on Sunday said there were estimated to be between 20,000 and 50,000 such pupils.

It quoted a senior government source as saying: “There has always been the freedom in this country for people to educate their children at home. Many people do it very well. But we need to know where the children are and to be certain they are safe.

“For every parent doing a brilliant job, there may be someone filling their child’s mind with poison. We just don’t know. We don’t have reliable figures.”

The government is reportedly considering proposals for parents to have a contact at local councils and to pinpoint how many are home-schooled.

A spokesman for the Department for Education said: “We are determined to tackle radicalisation wherever it occurs. We have provided Ofsted with extra inspectors to eradicate extremism in education.

“We are working with them to address their concerns about home education being exploited, while safeguarding the rights of parents to determine how and where to educate their children.”

The review comes after warnings about unregistered religious schools.

Earlier this month, the Ofsted chief, Sir Michael Wilshaw, warned that the safety and wellbeing of hundreds of children could be at risk as a result of being educated in schools illegally operating in several parts of England.

Three unregistered schools shut down by Ofsted in Birmingham in November were offering a narrow Islamic-based curriculum using antisemitic, homophobic and misogynistic materials. The conditions at the facilities also represented a fire risk, the watchdog said.