Ofsted says it has found evidence of children being taught in squalid conditions in three places in Birmingham which have now closed.
Anyone running illegal schools could face a jail term of up to 51 weeks.
Ministers are also consulting on plans for more regulation of places teaching for more than 6 to 8 hours a week.
Sir Michael Wilshaw, Chief Inspector of Schools in England, told the BBC this week that his inspectors were visibly shocked by the conditions they found.
It is understood that a total of 18 unregulated schools, mainly in Muslim communities in the Midlands, have been visited as part of an investigation in recent months.
Three places in Birmingham have been closed and the owners are being investigated under suspicion of running an illegal school.
Sir Michael said the cases uncovered were likely to be the "tip of the iceberg" and he was seriously concerned that children were at risk of being abused or radicalised.
Any place where children are taught for more than 20 hours a week has to register as a school.
Some places describing themselves as part-time education centres or "flexi schools"  are operating within the law providing support for home-educated children.
But Ofsted and ministers are concerned that some are taking advantage of the legal right to home educate to operate what are in fact illegal schools.
In a letter to the education secretary on Friday, Sir Michael suggested officials had been slow to take decisive action in the three places which Ofsted had closed with the help of the local council.
"This was achieved in spite of your officials providing, what I believe to be, confusing and unhelpful advice to the proprietors that they could now apply to register their provision."
The government has provided funding for a team of six inspectors whose job will be to investigate illegal schools.
While most of the places visited by Ofsted so far have been in Muslim communities, inspectors may also turn their attention to similar unregistered tuition centres operated by other groups.
"It will apply across the board, to any religious group whether Muslim group, Jewish group, or Christian group who wants to operate this sort of provision in unsafe accommodation, in unhygienic and filthy accommodation.
"It will apply to all religious groups, I want to make that absolutely clear," Sir Michael told the BBC.
The education secretary has now said she intends to go further.
"I have now asked Ofsted to prepare cases for prosecution against unregistered schools it has identified. For a child to spend a single day in one of these schools is unacceptable."
In order for a prosecution to be brought against an unregistered school the Education Secretary has to give consent.
The government consultation on further regulation runs until mid-January.
Education Secretary Nicky Morgan says anyone found running an illegal backstreet school in England will face fines or a prison sentence.