Local authorities have a duty in law to ensure all children in their area receive a suitable education, but they say their powers are limited.
Illegal schools can often have links to extremism or be housed in dangerous buildings, according to the Local Government Association (LGA), which is calling for the changes.
The LGA wants councils to have the power to enter homes and other premises to check the suitability of the education being delivered. Currently, they can only enter premises if there are specific concerns about a child’s safety.
The LGA also wants parents to be compelled to register home-educated children and would like to see a clearer definition of a “school” so that it is easier to classify and close down illegal schools when they are discovered.
Figures compiled by the BBC last year show that there are almost 37,000 children (out of a school population of 9.5 million) who are home educated, but that this figure has increased by 65 per cent in the last six years.
This increase has been linked by the Department for Education to an increase in illegal schools and an investigation by Ofsted found more than 100 illegal schools in operation.
In some cases, children have been taught in warehouses and old factories, and in facilities with open drains or no running water. Some illegal schools have also been linked to the teaching of extremist views.
Cllr Richard Watts, chair of the LGA’s Children and Young People Board, said: “In some cases, a child listed as home schooled can, in fact, be attending an illegal school. With limited powers to check on the work a child is doing, however, councils are unable to find out whether this is the case.
“Placing a legal duty on parents to register home-schooled children with their local authority would help councils to monitor how children are being educated, and prevent children from ‘disappearing’ from the oversight of services designed to keep them safe.”