Nobody should be surprised at official statistics showing that one in five women over 16 in England and Wales has been the victim of a sexual offence. Just before last week's report was launched and in response to a flurry of post-New Year accounts of harassment, the Everyday Sexism Project invited women to share their experiences of harassment on Twitter using the hashtag #ShoutingBack. Some 3,500 did so within the first five days.

The frequency of incidents reported is alarming: "Every day since I was 14 …" "I've lost count of the number of times …" "Called a bitch, whore, slut, slag on the street too many times to mention," were just a few of them. One woman said: "On street, bent to tie my shoe, man walks pass, sticks hand inside my top, into my bra & squeezes breast." Another described being "force kissed by a stranger in the street in broad daylight". One woman, a cancer patient, told how a man openly elbowed his friend as she passed and said: "You missed it. Totally bald. Proper dyke."

Many incidents happened on public transport, from "a man … putting his hand up my skirt and stroking my legs" on a packed tube, to a woman who tried to get off the train only to have a man grab her breasts and tell her "this isn't your stop, love". Another victim said a man "asked me to get off and f*** him … then tried to force my head into his lap".

The theme of harassers becoming aggressive upon rejection was also repeated again and again. One woman said shouts of "Hey … come here", switched to: "You whore, I'll beat you so hard," when she refused. Another described being "followed by a car of teenage boys who then tried to reverse into me when I wouldn't talk to them". In one case, "harassment started on the street, asking if I was married, ended with sexual assault on my doorstep at 3pm".

Threats of violence and sexual assault, such as "If I knew where you lived, I'd follow you home and rape you", were frequently reported, as were actual physical assaults. One woman was "Chased to my door at 11.30pm by two lads who 'Didn't want to hurt me.' I ran faster."

Nat Guest, a 26-year-old digital marketer from London, was walking home from a party on the morning of New Year's Day, when a man came up behind her, making "sexual overtures". When she didn't respond, he told her he had a knife and forced her to face a wall before masturbating into the back of her dress.

Although the police were supportive, the male officer said: "Usually I'd tell you to avoid walking around on your own late at night, but, you know – New Year's. You have to get home somehow." As a young woman in London, Guest experiences sexual harassment so frequently ("most days") that when she reflects on the incident, she says: "Theoretically, I feel angry about it but emotionally I don't feel much at all apart from resigned. But the fact that I feel resigned to this type of thing makes me feel angry."

Most worrying of all was the number of accounts that described the sexual harassment and assault of young girls. One said: "While walking home last year, a man inside a parked car ask[ed] me for a blowjob. I was 15 and in school uniform." One recounted "being told by my parents not to stand up for myself because that will get me raped".

Holly Kearl, founder of the US-based organization Stop Street Harassment, says: "Street harassment is often an invisible problem or one that is portrayed as a joke, compliment or the fault of the harassed person. In reality, it's a human rights violation."

As one of the male supporters of #ShoutingBack tweeted: "We have the power to stop street harassment. Don't do it. Don't let other men do it."

Until they stop, we will keep shouting back.