An early meme claimed “there are no girls on the internet”. The idea was that even the smaller number of users who identified as female were really male; they just hoped that posing as women would get them favourable treatment.

This was, of course – and excuse my lapse into technical language – total and utter bollocks. Women actually suffer disproportionately from online abuse (one study found that 72.5% of those reporting abuse were female), while their voices are under-represented overall. Women write fewer opinion pieces, and – if anything close to the pattern we see on newspaper letters pages is repeated online – leave fewer comments.

No wonder, then, that there are periodic questions about what we can do to make the web more female-friendly. The most useful parallel is with our real-world public spaces, where feminists have worked hard to stigmatise catcalling and street harassment.

In a new report, the former Labour policy adviser Charles Leadbeater has gone further, arguing for a “Mary Beard prize” to reward those who support women’s use of the web. He also draws a parallel with cities, arguing that their most productive spaces are “small enough for people to sit, linger in, make eye contact and chat”. A sign of an area’s safety, he argues, is “the presence of women and families – when they felt comfortable it was a sign that the space was good for everyone”.

Leadbeater is right. Improving the diversity of groups in public spaces benefits everyone, not just the minorities. Think of cycling: one of the best ways to make it safer is to encourage more people to do it. The aim is to get grannies and children sharing the roads with cars, not just the stereotypical “Lycra louts”.

The same principle applies to the internet. When I write about online abuse, I often get letters asking: “Why not just leave Twitter?” That’s like saying: “Why go out after dark? Or: “Why get on a night bus alone?” It is classic victim-blaming.

Mary Beard was by no means the first woman to get abuse after going on Question Time; Caroline Criado-Perez is not the first, or last, woman to be targeted for a harassment campaign online. Unless every woman leaves the internet (we’ll turn the lights out when we go, don’t worry), the problem will remain.

So what can be done? More laws are not the answer, although we do need the existing ones applied more consistently. It is absurd to jail a man for writing offensive but unthreatening comments on his Facebook wall, as happened to Jake Newsome in June - that can’t be a matter for the law.

At the same time, I’ve sat in a police station for hours on end while the officers argued over jurisdiction, based on the location of the computer used to read the offending messages. Another time, a victim of online abuse told me she had to explain to detectives how Twitter differed from email.

We are talking about old offences – making threats has been illegal for more than a century – but new technologies have made the police’s job much harder. Officers need more training and support, as well as procedures that can handle communications across borders, and via smartphones.

Whenever I feel pessimistic, though, I remember how quickly attitudes have changed to drink-driving (which was banned in 1966) and wearing seatbelts (compulsory since 1983). Half a century ago, 70 of men% and 40% of women smoked. Now the figure is less than one in five. In all of those cases, the change in the law was accompanied by a broader cultural shift. As a society, we came to look down on those who put their own and others’ lives in danger.

Something similar needs to happen to our attitudes towards online abuse. The police can, and should, prosecute the most serious offenders, but alongside that we need to eliminate “trolling” as a source of pride. Many persistent trolls believe they are free-speech martyrs, the Lenny Bruces or William Tyndales of our time. We should firmly establish the difference between “cutting-edge satire” and “telling a woman you will rape her on Twitter”.

We also need to encourage female-dominated spaces online, as these can provide a counterweight to the prevailing culture. TwoXChromosomes – a rare woman-led forum amid the sausagefest that is Reddit – recently protested over becoming a default sub-Reddit, meaning it would be more visible to the rest of the community. Its users feared they would be subjected to endless harangues about the “whorearchy” from self-styled pick-up artists, so they spent a week talking about periods and childbirth in the grossest terms possible, to repel interlopers.

The same goes for forums such as Mumsnet. In my twenties, I was sniffy about it – oh, how dreadful, mummies boring on about Boden and cupcakes – but now I see its value. Imagine you’ve just been made a geologist, and you need to find out about geology really quickly. Sure, you can read some geology books, but wouldn’t you also want to talk to some other geologists? Particularly in a society where geology is often devalued, and you are treated to endless conflicting messages about whether igneous or metamorphic rocks are better for your baby. (OK, that’s enough with the geology metaphor.) Until the wider internet becomes less exhausting, we need some safe spaces for women.

On that score, Charles Leadbeater’s idea seems promising. But it dodges the hard truth we have to confront if we want real change: making the web more friendly to women involves making it less friendly to those who hate or fear them.

An example. If you’ve ever read a feminist op-ed online, you might have noticed that the commenters seem, oddly, to speak with one voice: why is there no Men’s Hour? Why is it OK for Sharon Osbourne to joke about cutting off someone’s penis on a talk show, but violence against women is abhorrent? Why aren’t we talking about male circumcision? When will anyone address the unfairness of the “vaginamony” awarded to ex-wives?

All these comments are classic tropes of the men’s rights movement, which has had enormous success in bombarding the comment sections of websites – including this one – with points that veer from the valid but off-topic to the downright bizarre.

These are coordinated attempts to drown out women’s voices, and they are successful: research shows that hostile comments affect readers’ perception of the article. There is a clear freedom-of-speech issue here. Women are discouraged from speaking, sometimes with casual sexism and sometimes with violent threats, while our focus remains fixed on the rights of trolls and abusers.

Are we willing to condemn such tactics? Or do we believe, somewhere deep down, that men’s right to free speech is more important than women’s?

Anyone who can answer that is a worthy recipient of the Mary Beard prize.

Twitter: @helenlewis