Hundreds of women in Delhi have applied for gun licences following the gang rape and murder of a 23-year-old woman by six men in a bus in the city last month.

The news underlines the widespread sense of insecurity in the city, deep before the incident and deeper now, and the lack of faith in law enforcement agencies.

The ashes of the victim of the attack – who died on Friday after 13 days in hospitals in India and Singapore, and was cremated in Delhi in a secret ceremony under heavy security on Sunday – were scattered on the surface of the Ganges river, sacred to Hindus, in northern India on Tuesday.

The case has provoked an unprecedented debate about endemic sexual harassment and violence in India. Tens of thousands have protested across the country, calling for harsher laws, better policing and a change in culture.

Politicians, initially caught off-guard, have now promised new legislation to bring in fast-track courts and harsher punishments for sexual assault. The six men accused of the attack are to be formally charged with murder later this week and potentially face execution.

Indian media are currently reporting incidents of sexual violence that would rarely gain attention previously. In the last 24 hours these have included a teenager fleeing repeated abuse by her brother, who was allegedly assaulted on a bus by a conductor, a 15-year-old held for 15 days by three men in a village in Uttar Pradesh and repeatedly assaulted, an 11-year-old allegedly raped by three teenagers in the north-eastern city of Guwahati and two cases of rape in the city of Amritsar.

One case reported on Tuesday involved a woman, also in a village in Uttar Pradesh, who suffered 90% burns after being doused in kerosene, allegedly by a man who had been stalking her for months.

There were signs that a further taboo was about to be broken when one of India's best-known English-language television presenters asked viewers who had experienced abuse from a family member to contact her.

The rush for firearms will cause concern, however. Police in Delhi have received 274 requests for licences and 1,200 inquiries from women since 18 December, two days after the woman and a male friend were attacked in a bus cruising on busy roads between 9pm and 10pm.

"Lots of women have been contacting us asking for information about how to obtain licences. Any woman has a threat against her. It's not surprising. There are fearless predators out there," said Abhijeet Singh of the campaign group Guns For India.

Delhi police received around 500 applications for the whole of 2011, up from 320 the previous year.

Hundreds of women had come in person to the police licensing department in the city, the Times of India reported.

"We had to patiently tell them that one needs to have a clear danger to one's life to be given a licence. However some … said that with even public transport no longer safe in the city they just cannot take chances," an unnamed official told the newspaper.

There are estimated to be 40m guns in India, the second highest number in the world after the US. Licences are hard to obtain and most are illegal weapons, many manufactured in backstreet workshops. Official ownership levels remain low – three guns for every 100 people – but in recent years the number of women holding arms has risen. Most are wealthy and worried about theft or assault.

There are fears the attack will lead to further restrictions on women in India, who already suffer significant constraints.

Elders in Matapa, in the poverty-stricken Indian state of Bihar, banned the use of mobile phones for teenage girls and warned them against wearing "sexy" clothes. They claim the move will check rape cases and restore "social order". Other villages nearby are planning similar bans, locals said.

One member of parliament in Rajasthan, the north-western state, also called for a ban on skirts for schoolgirls to keep them away from "men's lustful gazes". Banwari Lal Singhal said private schools allowing students to wear skirts explained increased sexual harassment locally.

Matapa is in southern Bihar's Aurangabad district – the region from which one of the Delhi gang-rape accused, Akshay Thakur, comes. The order was issued after a formal meeting with villagers, council officials and school teachers on Sunday. "Almost every villager pressed us to ban the mobile phones use by the schoolgirls saying they are proving quite dangerous for the society and corrupting traditional values," the local village council head, Sushma Singh, told the Guardian on Tuesday.

Protesters were angered by the news. "Our sister will have died in vain if all that is happening after is our fear is greater and ladies are more unfree," said Deepti Anand, a 21-year-old student in Delhi who has attended demonstrations most days in recent weeks.

Additional reporting by Manoj Chaurasia