JFS has provoked anger from parents and pupils by teaching sixth formers that homosexuality can be "cured".
As part of the school's Jewish studies curriculum, pupils are shown a website from the American group JONAH - Jews Offering New Alternatives to Homosexuality.
It promotes the idea that homosexuality can be "mitigated and potentially eliminated" and sends participants on retreats such as "Journey into Manhood".
The JONAH website is introduced at the end of the textual study part of a lower sixth lesson on homosexuality and the Orthodox viewpoint.
Pupils have complained that, coming at the end of the lesson, there is no opportunity for debate and that the JONAH website was effectively presented as the authoritative statement of the Orthodox view.
One of the students at a recent lesson said: "We discussed whether someone chooses to be gay or not. Then there was the concluding voice of "the Jewish view", where we looked at Orthodox Judaism, which condemns homosexuality.
"At the end, we were asked what we thought about religious Jews who might hate themselves because their religion condemns being gay. The last slide on the PowerPoint was a picture and a link to the JONAH website, after we were discussing what gay Orthodox Jews can do, if they hate themselves."
The student said there was no condemnation or discussion of the controversy around gay "conversion", and no alternative group was mentioned. "I was appalled; it felt like it was saying, 'If you are having doubts, check this out'."
Another pupil who was in the lesson said: "If I were gay or worrying about my sexuality, sitting through that lesson, I would have been so upset. They could have advertised other organisations, which are not there to convert but to support whatever decision people want to make. I know most people were offended by it."
JONAH has run sessions in the UK. Rabbi David Mitchell of West London Synagogue said he was aware of people who had been involved in the organisation's "therapy". He said: "I find it deeply distressing that this group was referred to as part of a Jewish studies lesson, and have concerns about whether those preparing have students' best interests at heart, without referring to the damage JONAH has done."
Keshet UK, the lesbian, gay and transgender forum, whose co-chair Dave Shaw is an ex-JFS pupil, said it was "appalled" at the claims.
JFS head teacher Jonathan Miller said the JONAH website was intended to illustrate the different Jewish perspectives on the issue. Mr Miller said: "It is absolutely not the case that we promote JONAH. The teaching materials explicitly state that Judaism would utterly condemn homophobia and discrimination.
"The website is referred to at the end of the lesson, as another opinion, 'some Jews think this', to leave students with food for thought.
He said the school was looking into the issue of when it should be viewed during the lesson. "We are always reviewing what we teach after something like this comes up. There have already been discussions about it at the school. Absolutely, we will address it."