Just over a month ago, while doing research for a book about sexism, I opened an internet browser, typed "chat rooms for kids" into Google, and clicked on one of the first links that appeared. There was no registration process, no age check – I just typed in a made-up username, and immediately chat windows started appearing on my screen. Within seconds I had over 10 messages, almost every one of them reading: "ASL?" I wrote back: "What is ASL?" The answer came quickly: "Age. Sex. Location." I replied, claiming to be a 12-year-old girl from the US. The responses were immediate:

"Do you like sex?"

"Can I teach you?"

"Bra size?"

"Do you want to earn some extra pocket money?"

"Can I cu?"

While I hesitated, the messages quickly intensified: "My dick is long and hard" … "I am so horny" … "My wet dripping dick". I closed the windows. The whole thing took less than three minutes.

In the course of my work around violence against women and the forms it takes online, I've learned that it can get far more complicated – one expert recently told me about scenarios where men have sent messages to girls in chat rooms claiming to have uploaded a virus on to their computer … but they'll delete it on the condition of a video chat … if the girl does what she's told.

This week a Dutch children's charity carried out a very similar experiment on a much larger scale, using a computer-generated 10-year-old girl they named Sweetie. The results were chillingly similar, with 20,000 men contacting Sweetie over two months, and 1,000 offering to pay her to carry out sex acts on a webcam. But the reaction of law enforcement agencies to the revelations has been notably muted – though the UK's National Crime Agency has agreed to look at the information passed on by the charity, a spokesperson for European policing agency Europol told Reuters: "We believe that criminal investigations using intrusive surveillance measures should be the exclusive responsibility of law enforcement agencies." No promise of more concrete action has yet been forthcoming. This has only confirmed what we already knew – when it comes to online abuse, women and girls are on their own.

The internet is a fertile breeding ground for misogyny – you only have to look at the murky bottom waters of Reddit and 4Chan to see the true extent to which it allows violent attitudes towards women to proliferate. But, crucially, it also provides a conduit that enables many who hold those views to attack and abuse women and girls, from what they rightly perceive to be an incredibly secure position. Meanwhile, the police seem near-powerless to take action, social media sites shrug their shoulders, and women are left between a rock and a hard place – simply put up with the abuse as a part of online life, or get off the internet altogether.

These are not just nasty comments, or harsh criticisms – they are extreme, detailed and vitriolic threats of rape, torture and death. I have received messages detailing exactly how I should be disembowelled, which weapons could be used to kill me, and which parts of my body should be raped. When I ignored the threats, they intensified and proliferated, finding out information about my family members and threatening to rape them instead. They are the kind of messages that race around your head at night when you try to sleep, no matter how much you wrote them off as empty scare-mongering during the day. They make you hesitate to post online and change the way you use social media. And nobody seems to be able to do anything about it. Of the three rape threats I reported to police in recent months, two have already been dropped because the police are unable to trace the perpetrators. When I went to the police last year with a pile of abusive messages, including rape and death threats, they said they were unable to trace the perpetrators, even though I was able to provide IP addresses. When I showed them a specific website where users were being encouraged to send me abuse and threats, the police said it was US-registered, and therefore outside their jurisdiction.

Just like Sweetie and any other young girls her age venturing into shared online spaces, the answer seems to be an ambivalent shrug – this is just what happens to women online so you might as well get used to it. And woe betide you if you try to protest the apparent unfairness of that, because didn't you know that you are threatening free speech? Except that it's not a threat to free speech to suggest that once people have actually committed a crime (like threatening to rape or murder somebody, or trying to coerce a little girl into carrying out sex acts), they should be brought to justice for it. Threatening to rape somebody online is just as illegal as it is in a letter, or in person. Nobody is suggesting that the entirety of Reddit or 4Chan should be shut down, objectionable as some parts of them are.

But it's also telling that in all this hand-wringing over free speech, nobody is talking about the free speech of the women and girls who, as long as this continues to go unacknowledged and unresolved, are effectively being driven out of online spaces altogether.