More than 500 suspected illegal schools, educating thousands of pupils, have been identified in England over the past three years by the schools watchdog Ofsted, according to data published for the first time.

Some of the schools were in an appalling condition with rat traps, exposed wires and open sewers, Ofsted inspectors said. In one, pupils were left to play computer games all day, while in another inspectors found children in every classroom repeating religious texts with no other apparent education going on.

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In some cases local authorities were unwittingly sending children to unlicensed alternative provision. In one case, a council paid £27,000 a year for one of its students to be educated in an unregistered setting. Elsewhere, students were found being taught by teachers who had been banned and untrained staff who had undergone no employment checks, in buildings where hygiene and facilities were poor.

The data, released by Ofsted on Friday and never published before, shows the illegal schools task force has investigated 521 settings, and inspected 259 since January 2016.

Ofsted estimated that 6,000 children were being educated in the 259 unregistered schools it has inspected to date but, according to Ofsted’s deputy director, Victor Shafiee, who heads the unregistered schools taskforce, the figures represent the “tip of the iceberg”.

“All my inspectors tell me there’s still lots out there,” he said. “It just isn’t good enough that vulnerable children, isolated children, end up in these places where there is no oversight, no quality assurance, and they are out of sight.”

He said the most vulnerable children ended up being looked after by the least capable adults and as a result were “robbed of their life chances”. Parents were often misled, sometimes paying £7,500 a year for their child to be educated in an illegal or unregistered school.

“People hang on to the bottoms of lorries, and jump trains to get to this country because education is free. So why would you then send your child to an unregistered school and pay for them to go to these settings? It is something that I find unfathomable,” said Shafiee.

Almost a quarter (23%) of the unregistered schools Ofsted inspected were in London, with the rest evenly spread across the country as far afield as Cornwall and the north-east. A fifth (21%) were faith schools, including 36 Islamic, 18 Jewish and 12 Christian schools, and 28% were alternative provision for students who struggled to cope with mainstream education.

“As today’s data shows, this is not simply an issue with faith settings, nor is it limited to certain areas of the country,” said Shafiee. “Unregistered schools come in many shapes and sizes, and not all of them are run with malicious intent. But all children deserve the best.”

So far, 71 of the schools have been issued with a warning notice by inspectors; 15 of those have since closed down while 39 have changed the way they operate in order to comply with the law, and nine have registered as independent schools. So far, however, there has been just one prosecution, with two more prosecutions pending.

Ofsted is calling for greater powers to inspect unregistered schools and says the current legislative framework is inadequate, with inspectors unable to seize evidence, hampering potential prosecutions.

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Sue Will, an inspector on the unregistered schools taskforce, said she had been shocked by health and safety issues at some of the schools she had visited. She said she had seen portable buildings balanced on top of one another to maximise space. “Some of the buildings that we have been to are in really poor state – unsafe. We are not just talking about run-down places that could do with a lick of paint, we are talking about some not very nice places at all.

“Open sewers, rat traps in rooms … exposed electrical work. I’ve seen holes in walls and floors, I have seen locked fire doors, I have seen holes where children have probably punched plaster walls. That is the bit for me that I always find so shocking.”

An institution must register as a school – and therefore be open to inspection by Ofsted – if it is providing full-time education to at least five children of compulsory school age, or one child who is looked after by the local authority or who has special educational needs. The Department for Education (DfE) says that 18 hours or more a week constitutes full-time education so some providers avoid having to register by operating for 17 hours and 50 minutes per week.

The DfE said a new register for children not in school – recently announced by the government – would help councils to identify children in unregulated settings and intervene. A spokesperson said the DfE had already signalled its intention to legislate to enable Ofsted gather evidence to support prosecutions and help close down illegal schools.