Religious private schools that have repeatedly failed their legal equality duties have nevertheless been allowed to remain open – often with leaders still in key positions, Schools Week can reveal.

The latest batch of inspection reports from Ofsted list two such schools ignored rules set out in the 2010 Equality Act and failed to mention either sexual orientation or gender reassignment to their pupils.

One of these, Vishnitz Girls School, an Orthodox Jewish school in Hackney, north London, was warned both in October and November last year that it had failed to “pay enough regard to developing respect and tolerance” for those protected under the Act, especially LGBT people. A follow-up report from Ofsted in May found that nothing had changed.

The inspection in October established that school leaders were aware they were not meeting legal standards.

“The proprietor and leaders agree that the school’s policy on the protected characteristics means that the school cannot meet these standards,” concluded the report.

Another school, Bnos Zion of Bobov, also a Jewish school in Hackney, was similarly failed, for making “no reference to protected characteristics for sexual orientation and gender reassignment”.

Secularist campaigners have now claimed that the Department for Education, which is responsible for monitoring independent schools that do not belong to a formal association, is not being clear enough that schools will be closed if they do not abide by equalities law.

“If schools are not willing to meet the required standards and are found to be failing time and time again, proper sanctions must be implemented,” said Jay Harman, an educations campaign manager at Humanists UK.

If schools are not willing to meet the required standards and are failing time and time again, proper sanctions must be implemented

The finding follows investigations by Schools Week revealing the rising numbers of independent schools which have been issued improvement notices by the government in the wake of substantial regulatory failings.

At least 131 notices were issued last year – up on 120 from 2015 – and the government is now pledging to publish the documents online.

According to guidance on regulating independent schools, “schools that do not meet the standards must improve so they do meet them, or close”.

If a school found to be failing any of the independent school standards does not improve, the DfE has the power to take it off the register, making it a criminal offence to remain open.

Nineteen non-associated private schools – which means they do not belong to an association such as the Independent Schools Council – have now had their Ofsted reports released since the purdah was lifted after the end of the election.

Of the nine religious schools in that number, six either failed to meet the independent school standards or were given a ‘requires improvement’ or ‘inadequate’ rating from the inspectorate, Schools Week analysis shows.

Another religious school, All Saints School in Norfolk, failed because it was not fully meeting the needs of special educational needs pupils. It had failed before, in November last year, over health and safety checks.

Five religious private schools also had a previous Ofsted rating, after independent schools regulated by the DfE were included in Ofsted’s common inspection framework in 2015. But three of those five have seen their grade fall. In each case, their rating dropped due to a lack of progress for pupils.

The Marathon Science School in London and Buckhole Towers School in Dorset fell to grade three, while the New Life Christian Academy in Hull dropped to ‘inadequate’.

Two non-associated religious schools did manage to improve their grade: Al Huda Girls School in Birmingham and Cruckton Hall School both received a grade two.

Ofsted currently inspects the performance of 323 non-associated religious private schools, out of a total of 1,076 non-associated private schools.