From grandmothers to school-age children, and from buses to toy stores, this form of harassment is becoming increasingly prevalent – and it's time to take a stand

"When I was 13, a man sitting across from me on a crowded train took his penis out and fondled it. No one did anything."

There are some experiences that sound so extreme, so shocking, that there is a general consensus they must be very rare indeed. People would like to assume, understandably, that this story is a horrifying anomaly. But when I retweeted one woman's experience of being masturbated at this morning, the response was overwhelming.

A deluge of replies flooded in from women who had experienced the same thing. From grandmothers to girls who were six when it first happened, their reports came from London, Sydney, Frankfurt, Paris, Berlin, Barcelona, Brussels, Las Vegas, New York, San Francisco, Canada, Mexico, Ireland, Ukraine, Peru, and even Vatican City.

Within two hours, over 400 women and girls had come forward with their own experiences of being masturbated at. Many emphasised that these were not isolated incidents.

"Multiple occasions"… "At least once a year" … "Too often to count"

One woman wrote that she had brought up the subject with the women in her office at their morning meeting: "Practically all of us have a story of this happening".

The locations were as varied as the victims – from libraries to buses, courthouses to hotels, parks to toy stores.

Several women listed multiple experiences: "First time was in front of school aged 14, guy opposite watching us and masturbating. The second was on a bus in Italy; guy pressed against me and started rubbing his erection against me. Third time in Richmond Park, he had his trousers down."

Looking at the Everyday Sexism Project database, I realised that in the past two years, 525 women and girls have reported this particular experience. Certain words jump out from the entries, repeated again and again: "frightened"… "horror" … "frozen" … "fear".

A staggeringly high proportion of the entries, both on Twitter and to the Project website, specify that the victim was a child when the first incident occurred. The phrase "I was thirteen" recurs again and again, as do mentions of uniform and walking to school. One tweet read: "I was 11 walking home from school, man following masturbating. Police got involved and I didn't even know the word to explain".

When I spoke to a group of teenage girls at a careers event last year, they used the word "normal" to describe men masturbating on the tube in front of them while they were on their way to school in their school uniform. Girls are growing up in a world where this is such a widespread experience that some don't even see it as something unusual – just part of being a woman.

As with so many forms of gender inequality, harassment and abuse, many women reported that the problem had become so much a part of daily life that they simply modified their own behaviour to try and avoid it. Some described changing their route, or avoiding particular areas. One simply described it as a "hazard of bus travel". Some recalled reporting incidents to the police, but many more said they had never told anyone – out of shame, fear, or the worry that they wouldn't be believed. Some women kept quiet because, when they did try to tell someone what had happened, they were blamed, or asked: "What were you wearing?", as if they had somehow 'provoked' the incident.

The fact that so many victims are so young, and the sense of fear and helplessness they report, point to the important fact that, like rape, this is a crime that is about power and control. This is about men feeling entitled to sexual ownership of women's bodies in public spaces, about a sense that they are powerful and in control and a belief that they will not be punished. It is also about the normalisation of sexual offences within a culture that suggests women should just shut up and get used to it.

In reality though, these incidents are crimes and, if victims or witnesses feel able to do so, should be reported to the police. The British Transport Police launched Project Guardian last year specifically to deal with these kinds of sexual offences on public transport. Now police in the West Midlands are rolling out a similar scheme called Project Empower. Inspector Ricky Twyford, Manager of Project Guardian, stressed to me today that masturbation in public is a criminal offence in the UK. 2000 officers have been specially trained to deal with cases of unwanted sexual behaviour on the London transport network and, according to Twyford, reporting has already risen by 27%.

But while it's important to encourage reporting of these crimes, there's also a wider problem that needs to be addressed. Again and again, victims described witnesses turning away, ignoring the problem and failing to step in and help.

"Nobody said a thing" … "Nobody stopped him" …. "Nobody cares"

Of course it's not always safe to intervene, but in many situations, bystanders choose to look away when they could support a victim and send a clear message to perpetrators that what they're doing isn't acceptable. Every time a perpetrator gets away with masturbating in front of a woman or girl and witnesses turn away, it sends the message that they can get away with it again. Meanwhile, victims are reminded that they shouldn't expect any help, because this is just the way things are. We all have a role to play in standing up, stepping in, and shattering the illusion that this (and the related sexual harassment women all too often face in public spaces) is somehow a 'normal' part of our society.

If you think that being masturbated at is a rare experience, today's torrent of tweets should change your mind. It's time to face up to the prevalence of the problem. It's time to take a stand.