Only one person knew that Svetlana was gay when she wrote to Deti-404, a Russian support group for lesbian teenagers. In her letter, the 16-year-old described a life of hiding her sexuality in a small town in central Russia where a man had been killed for being a homosexual. "I am scared that they will find out about me and lynch me. Sometimes I want to cry out: 'Accept me for who I am! Or at least be tolerant of me'," she wrote.

Deti-404, which takes its name from the error page that appears when a website does not exist, was set up by Lena Klimova, 25, after she wrote an article about the plight of LGBT (lesbian, gay, bisexual and transgender) teenagers. She had no plans to do anything further, but then she got a letter from Nadya, 15. "Nadya was hounded at school, her mother didn't support her," said Klimova in an interview with the Observer. "She decided to die, accidentally read my article and didn't do it."

After Klimova had spoken to Nadya by telephone and understood the depths of her despair, she asked herself: "Why does nobody ring alarm bells, not scream, not shout about it on every corner?" She added: "Many of them close in on themselves, they don't tell anyone. They are scared of parents and classmates. If they open up, parents sometimes beat them, insult them, throw them out, take away their phones, ban them from going on the internet and even lock them up in a psychiatric clinic."

The small support group is one of the few for young gay people in Russia. It would also seem to be exactly the thing that the controversial anti-gay law passed by the Russian parliament wishes to crack down on. The law, similar to the section 28 law that was passed by Margaret Thatcher's government in 1988, bans the dissemination of "propaganda of non-traditional sexual orientation" towards under-18s and imposes fines on anyone convicted.

The legislation has caused an outcry in the west, leading Stephen Fry to compared the situation of gays and lesbians in Russia to that of Jews in Nazi Germany. In an open letter to David Cameron and the International Olympic Committee, Fry called for the Winter Olympic Games in Sochi next year to be taken away from Russia. But the prime minister, in a Twitter reply, said he thought prejudice was better challenged by attending the Games rather than boycotting them. Last week the IOC obtained assurances from the Kremlin that competing athletes would not be affected by the law. But for Russia's LGBT community, the latest move has simply ratcheted up the pressure still further.

When she set up the group, Klimova surveyed 115 LGBT teenagers all over Russia, creating a closed forum for the teens to interact. Her survey showed that a number had thought of suicide. Fewer than half had come out to their parents. "It is only on the internet that they can find somebody to speak to," she said. "The feeling that most of these children feel is constant fear."

Some of the teens' letters are shown on the Deti-404 page, with pictures of the authors with their faces obscured so that no one can recognise them.

When a teenager gets in touch, if necessary Klimova helps them speak to a sensitive psychologist. "I tell practically all of them that they are needed, unique and invaluable. I am not pretending. It is true," she said.

Teenagers in smaller towns – where there are few, if any, openly out people and no gay scene – have it the hardest. "Our school is considered progressive, but it is quite normal for teachers to say that homosexuals will burn in hell," wrote one 16-year-old from a small town "which isn't even on the map".

Svetlana was once having dinner and on one of "the damn channels of this no less damnable country there was a show about LGBT". She remembers the scorn and contempt of her mother. "She calls homosexuals – and that means me too – mutants." Her father said he was ready to go out with his gun and kill them, while her older sister said they should be treated in psychiatric hospitals. Svetlana has still not come out to her family.

Homosexuality was only legalised in Russia in 1993. Now the new law is in danger of breaking the morale of some of those who see only a future of concealment and unhappiness. "When they passed the law, all the teens I know were in despair. You know, in reality, the law is aimed at them," said Klimova.

Vicious physical assaults have continued with depressing frequency. A man in Volgograd was murdered after revealing to friends that he was gay. A vigilante group lured young teens on social media by pretending to be older men looking for sex and then humiliated them on videos which they uploaded to the internet. "LGBT are called paedophiles, carriers of HIV/Aids, whatever you want, but not normal people. Of course people feel that and of course there are more hate crimes," said Klimova.

She is certain that there will be no boycott of the Winter Olympics. But she does have one plea. "Sportsmen can go to the opening ceremony with a rainbow flag in support of Russian LGBT. It would be very valuable," she said.

Some names have been changed.