The number of unregistered yeshivot in Stamford Hill has climbed to more than 30, despite attempts to regulate them, according to an education authority.
Hackney Learning Trust, run by the local council, has updated its list from earlier this year of 28 such institutions,to 33 at the latest count.
Efforts to persuade local yeshivot to register with the secular authorities appear hamstrung by a legal loophole.
Although an institution teaching children aged 16 or under for more than 20 hours a week is required to register with the Department for Education (DfE) as a school, yeshivot have argued they do not meet the technical definition of a school and so remain outside the scope of the law.
A Hackney Council spokesman said: "We are left in a bit of a Catch-22. There has to be some clarity: is it a yeshivah or is it a school? It is not within our powers to determine. This is one of the issues we are in dialogue with the DfE about. "
We want to ensure the health and safety of children
The council has called for greater registration powers which would extend to institutions other than schools.
In response to a DfE consultation in January, Hackney said it remained "extremely concerned about the potential for safeguarding concerns which remain unaddressed due to a complete lack of engagement on the part of both the individual out-of-school settings and their proprietors, and also the community in which they operate".
It gave examples of shortcomings found by Ofsted inspectors on some premises, including no fire-doors, dangling wires, raw meat on a dirty kitchen surface and unhygienic toilets.
The council voiced concern about inadequate secular education in institutions where the emphasis was on "Kodesh" - religious studies. But Rabbi Avrohom Pinter, of the Union of Orthodox Hebrew Congregation, said over the past six months "there has been a lot of work between the council and the community to promote health and safety.
"We all want to ensure the health and safety of our children should not be compromised. This is paramount to us".
Courses provided by the council in conjunction with the Orthodox charity Interlink had been well-attended, he said.
Around 1,000 teenage boys from the area are estimated by the council to be learning in unregistered yeshivot.
New rules came into force last month making it easier to trace their whereabouts. Registered independent schools now have to inform the council of the destination of children who leave them. But the hands of the education authorities remain tied by the current law.
Although one Charedi primary school was shut earlier this year on DfE orders, the children are now being home-schooled, according to their parents. There is no requirement to register children in such circumstances.
Hackney Learning Trust was also worried about the educational standards of some registered Charedi independent schools that have failed Ofsted inspections.
"In the interests of all parties, there needs to be some greater clarity about what should happen to a setting that receives two or three consecutive inadequate ratings," a council spokesman said.
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