Britain's schools inspectorate Ofsted says it has found evidence of children being taught in squalid conditions in at least three places in Birmingham which have now closed.
UK education secretary Nicky Morgan has said that anyone running illegal schools could face a jail term of up to 51 weeks.
"I have asked Ofsted to prepare cases for prosecution against unregistered schools it has identified," she said.
It is understood that a total of 18 unregulated schools, mainly in Muslim communities in the Midlands region of the country, have been visited as part of an investigation in recent months.
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Sir Michael said his inspectors were visibly shocked by the conditions they found.
The government has provided funding for a team of six inspectors whose job will be to investigate illegal schools.
"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 said.
The schools inspectorate will also be able to prosecute Islamists running registered madrasas but who fail to heed warnings to stop teaching extremist ideology, misogynistic or homophobic ideas or anti-semitism, the newspaper said.
Under already existing powers Ofsted can close down schools.
There are an estimated 2,000 madrasas in the UK attended by about 200,000 children, according to a 2011 report by the Institute for Public Policy Research.
The report found that while many madrasas make a valuable contribution to British society, "a significant minority" do not have adequate child protection or teaching standards.
Ministers are also consulting on plans for more regulation of places teaching for more than six to eight hours a week.