On a rooftop in a down-at-heel part of the northern Indian city of Lucknow, Preeti Verma eyes the man in front of her warily, sizing him up, looking for a sign of weakness. There are other women here, too, egging her on. They edge closer, encircling the man. Now the young woman darts forward, swivels and kicks out. The man doubles up and falls backwards, the air escaping his lips in a rush.

The watching women collapse in fits of giggles as the tension falls away. They are the Red Brigade, a group of intelligent and sassy young women in vivid scarlet uniforms who are leading the fight back against a rising tide of sexual abuse in India.

Today they are running through moves with their gym instructors, preparing themselves for the battles ahead. But this is not a game, as the men who have made their lives a misery are beginning to discover to their cost.

Having formed a little over two years ago with the aim of defending themselves against the endemic sexual abuse they faced every day in the Madiyav slum, in the capital of Uttar Pradesh state, they were galvanised by the gang rape and murder of 23-year-old medical student Jyoti Singh in Delhi in December.

India is in the grip of rape fever: some describe it as an epidemic. Since Singh's death, every day has brought new reports of atrocities against women from across the country. Foreign tourists, too, have been targeted and the attacks have been blamed for a 25 per cent fall in visitor numbers in the first three months of the year.

In Delhi, reports of molestation are up 590 per cent year on year and reported rapes have risen 147 per cent.

Clearly this is partly the result of a greater confidence among women to report such attacks and put pressure on a previously indifferent police force to record their allegations. However, there is also a feeling among many Indian women that such abuse has been on the rise, the result of a surplus of frustrated young men with little education or prospects of finding a wife, a predicament that is due to an obsession among many Indian families with producing sons and the widespread abortion of female foetuses. That surplus has been coupled with greatly increased access to pornography, on mobile phones, which is likely to have adversely affected the way men regard women.

Singh's death was a spark to the tinder box. She suffered horrendous internal injuries when she was raped and tortured by six men on a bus as she tried to get home from the cinema. Protests swept the nation. Something, women agreed, had to be done.

And so here are the Red Brigade, and they have had just about enough of being groped, being gawped at and much, much worse. They all have stories of abuse.

Pooja, 18, laughs as she describes how they dealt with one boy who pushed them too far.

"He had been taunting the girls, always calling out to them, saying he could have sex with them whenever he wanted," she says. "We all went to him and told him to stop, but he didn't listen. One day, when all of us were there, he said it again.

"We all stopped and turned round, and we surrounded him and grabbed his arms and legs. He thought it was a joke, but we were not kidding. Four of us lifted him in the air and the others started to hit him with their shoes and fists."

The boy's friends, terrified, had run away. One went to the boy's house and told his parents, who ran out to the field to remonstrate with the Red Brigade.

"They wanted to fight but we told them what he had been saying to us and after they had listened they realised how bad he had been and then they beat him, too."

Men who molest the Red Brigade now know that the boot is on the other foot, and that boot is heading for a very painful place indeed.

"We've caught a lot of men recently," says 17-year-old Sufia Hashmi. "I joined up because men always used to pass comments on me and touch my body but, now we beat them, the men cannot do anything and they run away. You feel powerful and you feel good."

Most of the 15 core members are in their mid to late teens, though they have also picked up a very determined 11-year-old who sports a powerful right hook at trouser height. And there are dozens of other girls who join the group when they can, many stepping out of school uniforms to don the stylish black salwar (trousers) and red kameez (shirt) that says: "Don't touch".

Their founder and leader is 25-year-old teacher Usha Vishwakarma, whose small family home the women use as a base. Vishwakarma was 18 when a fellow teacher demonstrated to her the danger faced by young women in the country on a daily basis.

"He grabbed me and put his hands round me and tried to open my belt and trousers," says Vishwakarma, sitting in the bare-brick front room of her small house. "But I was saved by my jeans because they were too tight for him to open and that gave me a chance to fight, so I kicked him in the sensitive place and pushed him down and ran out of the door."

When she told the school authorities that the man had tried to rape her, no one would take her seriously. They told her to forget it and to stop causing trouble.

The experience left her traumatised and for two years she did nothing. But little by little her confidence came back. In 2009 she set up her own small school for local girls in an outbuilding next to her family home.

All around her she saw more and more young women suffering the same abuse she had faced. It was threatening to wreck the prospects of her young female students.

"Parents were telling girls to stay in their homes so there would be no incidents. They said, 'If you go to school boys will be troubling you, so stay home and there will be no sexual violence,'" she says.

"But we decided we would not just complain, we would take the lead and fight for ourselves."

There is plenty to fight against. The number of reported rapes (in 2011, the last year for which figures are available) rose 9 per cent from 2010 to 24,206, while conviction rates have fallen 44.3 per cent over the past 40 years.

"It is in the minds of men that girls are objects and it has been like that always," says Vishwakarma. "Religion shows women as very powerless and that [those] who are strong can do anything."

She sits on a bed that dominates the sparsely furnished room. Against the far wall is a table on which sits a television and a pile of the placards the group carry with them when they go out to protest on the 29th day of each month, to mark the date of Singh's death. The slogans read: "Stop rape now" and "We want safety".

Pooja describes how another young man made suggestive comments to her every time he walked past the house and saw her sitting on the step.

"He was always saying we looked sexy and asking us to go with him and singing sexy songs, even though we told him to stop and not to talk to us like that," she says.

"One day I decided I had had enough so I told the others and we went to his home. We did not have to beat him ourselves this time because as soon as we arrived the boy ran away. His parents realised he had been very bad because the Red Brigade had come and when the boy went home they beat him. Now when I see him in the street he looks straight ahead and cannot look at me.

"First, we go to complain to [a offender's] parents and if they listen that is a good thing. But if they won't listen then the Red Brigade comes and together we catch the boy and we beat him."

Preeti sits on the edge of a bed and gazes out of the door at the pigs kicking up dust as they trot past along the dirt road. Her family are too poor to own a toilet, she says, so she has to go out into the fields.

When the 17-year-old would go out to relieve herself, the man in the neighbouring house would throw stones at her, to try to scare her into jumping up.

"He wanted to see my body," she says. "I said to him, 'What are you doing? You are shameless! Don't you have a mother and sister in your house?' But he replied that his mother is for his father, his sister is for her husband and that I was for him."

So the Red Brigade went to visit him, and after that Preeti had no more trouble from the man.

Afreen Khan, 16, says her own brother tried to molest her, with the help of a neighbour, when she was just nine. When she joined the Red Brigade, it gave her the courage to speak out and now he has been cast out of the family.

"Before joining the Red Brigade men used to abuse me and I used to cry. But after joining I have been able to revolt and I have even beaten some of them and now I can walk out alone, even at night, and no one teases me. They leave me alone. That's the courage that joining the Red Brigade has given me."

It is clear that the message is getting through. When the Red Brigade stride through the local market in their uniforms, men step aside, like a pack of wolves who have just discovered the sheep are armed.

There is still a long way to go, however, before women in India can feel safe.

"In the electronic era there are pictures everywhere of girls being treated like objects," says Vishwakarma. "It is now very simple to see pornography and it is feeding the hunger for sex. The men think that if you are looking sexy then you want sex.

"I alone cannot change it but we can change it together. We are working with teenage girls and explaining that men have to be responsible. Sex is important but they have to honour us, they have to respect us and change themselves. They cannot think girls are lower than boys.

"Everyone stops their daughters going out at night but I say to them, 'Why are you not stopping your sons going out?' They are the problem."