The comedian Kate Smurthwaite received 2,000 abusive tweets for objecting when a men’s rights activist called her “darling” in a TV debate. Some called her “bitch”, “slut”, “harpy”; some were explicit threats of violence and rape.

After going on Question Time, the historian Mary Beard received hundreds of messages attacking her appearance. And the scientist Emily Grossman received so many hostile, sexist tweets when she talked about sexism in science, she was forced to take a break from social media.

But it’s not just public figures. I’ve heard stories of teenagers who have stopped going into college, women who have withdrawn from social media or been forced to change their work after being bombarded with online attacks.

We shouldn’t stand for this. The internet is an amazing thing – a way to give a voice to the voiceless, reinvigorate democracy, inspire debate. A third of us use Facebook. A fifth of us are on Twitter. Social media is where we live our lives: work, play, gossip and chat – our new streets, offices, pubs, parks and public spaces. And that means everyone should be part of it.

The internet has to be a way to speak truth to power and to hold the powerful to account – not a way for the powerful or the abusive to silence the truth. We need to be able to express anger, disagreement or contempt in an argument – and it’s really important in a democracy for those in power to see the strength of feeling about decisions they take.

But, just as we would on the streets, in the pub or at work, we have to challenge misogyny, racism, homophobia and intimidation or threats against others that are designed to silence debate.

We need new guidelines and capacity for the police and prosecutors to deal with violent threats

Let’s be honest: technology and new media move fast, and this is all so new that no one is sure where we should draw the line, or whose responsibility it is to act. And I won’t pretend to know all the answers. But as Stella Creasy, who has led campaigning in this area, has argued, we can’t keep ignoring it because it’s hard. So here’s where the debate should start.

First, we need new guidelines and capacity for the police and prosecutors to deal with violent threats, hate crime and stalking, which clearly break the law. Too many people feel they don’t get the protection they need.

Second, institutions could do more. Pubs give people warnings if they are being abusive, or kick them out if they are harassing other customers. The new social spaces – social media and newspapers that publish online comments – need to think about their responsibilities too. Membership organisations can set standards of behaviour they expect. The Labour party has rules to prevent sexism, racism or bullying in meetings; it’s time to apply the same principles online. Why don’t the Tories, SNP, Lib Dems and Ukip do the same?

Third, more support and advice. Those who have suffered the worst persistent abuse say they feel very alone. But right now the rest of us don’t really know how to help or stand with them – whether to confront any online sexism thrown at us or ignore it. I’ve always tended to ignore it, feeling I can’t really be bothered to give it any oxygen. But @EverydaySexism has shown the power of shouting back and speaking out.

And fourth, we need to do more to prevent the next generation thinking online misogyny, racism or hatred is OK – and to prevent it from contaminating offline relationships too. We need compulsory sex and relationship education in schools to promote respect in relationships and zero tolerance of violence or threats.

But whatever the answers, we can’t ignore this issue any more. A century ago, the suffragettes fought against the silencing of women in public and political life. In the 70s and 80s feminists began the campaign against the violence, threats or harassment that silenced women in the home or on the streets – founding the first refuges and organising marches to “reclaim the night”.

Each time, campaigning women challenged and changed culture. We need to do the same again now so women are not silenced on the new streets of social media, so no one is drowned out by bullying and abuse.

It’s time for women and men to stand together against sexist abuse, misogyny, racism and violent threats online – so the web can be the amazing democratic space we need it to be. It is time to reclaim the internet.