A Jewish state school is not breaching the school admissions code by requiring families not to wear leather or lycra, access the internet or use online entertainment, an adjudicator has ruled.

This week the office of the schools adjudicator partially upheld a complaint against Yesodey Hatorah Senior Girls School in north London, which has been at the centre of several recent scandals.

The adjudicator said that a requirement for pupils' fathers to belong to a Charedi synagogue was contrary to the law.

It also said its admissions rules lacked clarity and objectivity. It said rules on children's families wearing "flashy" coloured clothing, "discreet" make-up, "unsuitable home entertainment", "trendy" shoes and "very long" skirts were ill-defined.

The adjudicator said some parts of the school's requirements were "not sufficiently clear that parents can 'easily understand' if they meet these requirements". But it allowed the substance of almost all of these rules to stand once the governing body had clarified the meaning behind them.

For example, the adjudicator accepted the governing body's decision to remove the word "flashy" in the sentence "the wearing of flashy or very brightly coloured clothing is forbidden". It also accepted its definition of "trendy" shoes as those made of "leather and lycra".

It said the school's governing body had responded "very constructively" to its objections on clarity and objectivity. The only suggested change to the rules which the adjudicator rejected was on make-up, where it said a new requirement to be "conservative" was "no more objective" than the requirement to be "discreet".

The adjudicator's report also said the fact there were differing requirements on the dress of fathers and mothers did not breach the 2010 Equality Act.

"Within some religions, there are different practice requirements for men and women. There is nothing in the legislation that says that such practices cannot be taken into account, provided the requirements of the code, relating, for example, to their clarity and objectivity, are adhered to."

Yesodey Hatorah's admissions code forbids the families of applicants from wearing short skirts, long wigs, bright clothes, low-cut blouses, short sleeves and casual clothes. It also bans families from watching television and accessing the internet.

The school says that the requirements are in line with "the spirit of modesty and holiness" demanded by "the ethos of the Union of Orthodox Hebrew Congregations".

In June the schools inspectorate Ofsted found that Yesodey Hatorah had deliberately undermined pupils' safety, taught a narrow curriculum and failed to promote tolerance.

Earlier this year it was also revealed that the school had censored textbooks, including by removing references to homosexuals from a section of a textbook about Nazi policies and removing pictures of women socialising with men.

In 2013 the exam board OCR found that the school had obscured questions on evolution in 52 papers in two GCSE science exams, meaning they could not be answered, after the National Secular Society raised concerns.

The following year the schools minister wrote to the school after the NSS raised new concerns that it had advised pupils not to answer exam questions on topics such as evolution and human reproduction.

NSS education and schools officer Alastair Lichten said the adjudicator's decision was "an astonishing reminder of both the litany of failures at this school and their contempt for the educational and religious freedom of their pupils and families".

"It defies belief that a state-funded school can be allowed to impose such draconian and discriminatory standards on children's families and to shield children from life in modern Britain to this extent.

"The adjudicator's decision also shows the folly of allowing religious groups to run schools. The admissions code only allows schools to make such ludicrous demands because it allows them to adopt policies which fit within a religious ethos. If faith schools were rolled back the state could hold schools to consistent standards on admissions regardless of religion."

The NSS campaigns for a moratorium on state-funded faith schools, followed by the rolling back of religious control in schools, through its No More Faith Schools campaign.