Laura Bates had an unsettling moment recently after clicking on an article entitled "How to tell if your cat loves you". Scrolling to the end, the Guardian columnist and Everyday Sexism founder noticed that there were more than 800 comments. "I felt immediately that kind of clench in my stomach that I feel when there are 800 comments on my own articles," she says. "My eyes sort of drifted down them and it was things like, 'Thanks so much for writing this lovely article' and I was like, 'What? People say things like that?'"

The most benign of Bates’s online critics call her humourless. Yet over afternoon tea in London, where we are taking a break from the Southbank Centre’s WOW – Women of the World Festival, she is remarkably good-humoured. Especially given the number of rape and death threats she has received since setting up the Everyday Sexism Project in 2012 as an online safe space for women to share their stories of discrimination and harassment – and hundreds of thousands have.

When Ashley Judd, Uma Thurman, Gwyneth Paltrow and others called out sexual harassment using the #MeToo hashtag last year, it seemed the apotheosis of her idea. Yet Bates remains cautious. “It’s certainly an exciting moment, but we need to make sure that the momentum translates into real change,” she says. “Throughout history the women’s movement has seen backlash after backlash: every time it seems like we’re making some progress, the patriarchy reasserts itself.”

Consider as an example the election of President Donald Trump in the United States. “What has been quite shocking and galvanised many people into action is the realisation that he didn’t get into office in spite of his sexism and racism and Islamophobia – he got into office because people agreed,” says Bates.

What she has tried to achieve with her new book Misogynation: The True Scale of Sexism, which is an anthology of her writing for The Guardian, is a joining of the dots between casual sexual assaults of the kind that led her to found Everyday Sexism and the assumptions and power structures that underly them.

“I was sick of being told that it’s OK to talk about some of these issues but don’t make a fuss about others,” she says. “It’s OK to talk about rape and sexual violence but don’t make a fuss about sexual harassment. It’s alright to discuss the underrepresentation of women in politics but don’t make a fuss about media sexism.”

Most of us barely register a news story that a woman has been killed by her partner in an “isolated incident”. But for Bates, who spends her days reading stories of sexism, everywhere from the home to the streets we walk down, violence against women is hardly isolated. “Until we see the connections between all of these different issues, we can’t solve any of these problems,” she says.

The problem is that the bigger picture is so vast. Misogynation links sexist toys like Engineering Barbie (sold with a pink plastic washing machine and clothes rack) with the underrepresentation of women in science, technology and engineering. It draws a line between airbrushed advertising images and pressure on girls as young as 10 to lose weight. It argues that blaming a murdered female backpacker for travelling alone feeds into the idea that violence against women is inevitable.

To the converted it all makes perfect sense, but others will read it and cry hysteria. A review in the London Evening Standard called the book a "relentlessly grim picture of what it's like to be a woman today", mocking the idea of an "epidemic" of sexual violence. That reviewer may have had an axe to grind, having titled her own book Women vs Feminism – a volume for which there is surely a special shelf in the special place in Hell reserved for women who don't help each other. But her argument is one that we hear a lot: this is all terribly exaggerated, and women need to shut up and get on with it.

Bates disagrees. “You can’t solve a problem if you can’t label the problem,” she says. “You can’t fix something if people don’t even acknowledge it exists.” The revelations about Harvey Weinstein, whose abusive behaviour, which he denies, seems to have gone unchecked for decades, show how true this is. Now, she argues, the solution will come from all the people who have listened and been shocked: “The problem is collective and it cannot be fixed by individual actions.”

For her part, Bates is using posts from Everyday Sexism in talks at schools and workplaces. The stories of women on buses and trains were used to retrain 2,000 British Transport Police officers, increasing the reporting of sexual offences on the transport network by 35 per cent. And Facebook changed its policy on moderation of sexual violence images after an Everyday Sexism campaign.

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It’s a strong record, but has come with a personal cost. Bates and her husband had to take security measures at their wedding after details were stolen from her Facebook page, and at one point moved out of their flat after receiving violent threats from someone who had found the address.

The book reveals that at one point she consulted a counsellor. “One of the difficult things is there’s not a lot of empathy,” she says. “When you say that people’s fantasies of raping and abusing you are having a mental health impact people say, ‘You know it’s just to scare you?’. As if you can switch it off in that case.”

I wonder what kind of person you have to be to stick with a project like this, but Bates quashes the image of herself as a virtual Joan of Arc. "The honest answer to that is that I had no idea what I was getting myself into. I thought I was setting up a tiny website and I would carry on with my own life. If I had known what I was getting myself into, it probably wouldn't have started."

She puts her success down to the sheer volume of posts on her site: 100,000 in the first three years alone. Yet she understands enough about media sexism to know that her voice is heard where less attractive or non-white colleagues’ might not be and she does her best to compensate, for example, by demanding diversity on panels or TV and radio programmes where she is invited to appear.

As an example of how factors such as race and religion can exacerbate sexist treatment, we talk about discrimination faced by Muslims in the UK, especially in relation to the hijab. “We hear from Muslim women who have been harassed, threatened, spat at and physically assaulted in public space, including having their headscarves forcibly removed,” says Bates. “For many, race is another intersecting issue.”

Despite all these layers of complexity, Bates is clear about how to start solving the problem. “You start in schools because it’s the most effective way to reach everybody before it’s completely normalised,” she says. “Because people will go on out of that environment to move into politics, to move into academia, to move into the media and they will take those ideas with them.”

Later we return to the Wow Festival, where Bates is headlining the Friday-night programme alongside the Black Lives Matter founder Patrisse Khan-Cullors, and gives the crowd a similar action point. “It’s easy to feel disempowered but every one of us can have an impact in our own small sphere,” she says. “Every one of us can have those conversations with the young people in our lives and make a difference that will grow with them.”

Misogynation: The True Scale of Sexism by Laura Bates is out now, published by Simon & Schuster