An unregistered strictly Orthodox school which shut after an investigation by the education authorities has reopened, according to Ofsted.

The inspection service says it has issued warning notices to “three suspected unregistered Jewish schools” in Hackney, north London, since launching a task force to crack down on unauthorised schools last year.

“One has subsequently registered with the DfE and is now operating within the law,” an Ofsted spokesman said. “One unregistered school closed but has since reopened. The unregistered schools that continue to operate remain under investigation.”

It declined to name the schools involved.

Hackney Council believes more than 30 unregistered Charedi educational institutions operate locally – although strictly Orthodox community sources said the figure was lower.

But Charedi representatives say the institutions in question are yeshivot and fall outside the legal definition of a school.

Amanda Spielman, Ofsted chief executive, this week called for tougher laws to regulate independent faith schools. “It is clear that weaknesses in current legislation allow some organisations to teach school-aged children religious texts full-time, while avoiding registration and proper scrutiny,” she said.

Ofsted would do “everything we can to make sure they comply with the law or are closed. But action is also needed now to protect the children who attend these places.”

A DfE spokesman responded “unregistered schools are illegal and unsafe...There are already powers in place for local authorities and the police to safeguard children and intervene where they are not receiving a suitable education. We will support them in using these powers.”

The previous government had promised to introduce new powers to inspect part-time educational institutions that were not classified as schools – but although the consultation ended a year ago, no legislation has come forward.