Ms May also refused to come clean about whether spies were collecting medical records and other sensitive personal information.
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.