Like many people, I've learned to live with a generalised, low-level irritation about the content of some of the tabloids. The sexism, the xenophobia, the hypocrisy: you wish you could change these things but, for the most part, you accept them as the price you pay for a free press.

But on Monday night, years of irritation were transformed into rage for me by the suggestion that one tabloid, the News of the World, had paid a private investigator who hacked into the mobile phone of a missing 13-year-old girl, Milly Dowler. Worse, it is alleged that he deleted messages from her voicemail, giving her parents false hope that she might be alive – with the tabloid all the while running interviews with those parents in which they spoke about their hope.

There is only one sane reaction to this: utter revulsion. I knew that hundreds – maybe thousands – of people would be feeling the same way, and I also knew that this time it wouldn't only be the lefties, the liberals and the hand-wringers who would want something to change, who would be looking for something they could do. It would be all of us.

That evening I began tweeting (@the_z_factor), knocking around a few ideas with friends: egging NewsCorp's offices? Going to the shops on Sunday and turning over all the copies of the paper? It didn't seem enough. The only way to show the company how people really felt was by hitting them where it hurts: their wallets. And while I didn't think I could reach their regular readers to ask them not to buy the paper, I realised who I could influence, with a following wind and enough people behind me: their advertisers.

I went on to the News of the World's website. There were a couple of advertisers there, but most were behind the paywall. I tweeted them anyway. Immediately, my tweets were retweeted. And again. I roped in Andy Dawson (@profanityswan) – he was angry too, I knew, and more importantly he has a big following on Twitter. He researched more advertisers for me, and we began sending out tweets, telling people to send their own messages rather than retweeting ours for maximum effect. I made a Word document, stored it online and started sending out links to it. The activity was building; I was transfixed by my computer screen, and the dog didn't get an evening walk.

Tony Kennick (@thegreatgonzo) got involved. He had an idea: we could build a web page with "tweet me" buttons, to make things even easier for people. By Tuesday morning it was up and running, and by 11am Roy Greenslade had linked to it on his blog.

That's when things really started to take off. Messages of support began flooding in, as well as offers of help; @EroticPuffin looked up email addresses for executives at the companies and supplied an Excel file ready for mail merge, and various people sent new advertisers for us to add to the list and new ways for people to make a difference.

It's times like this when Twitter really comes into its own. As a truly democratic forum, everyone can get involved and have their say, and it's easy to share information and ideas. And because it's all so public, it's very hard for companies to ignore public pressure or hide behind rhetoric. For every 5,000 tweets with a funny cat photo there's a moment like this, when Twitter remembers what it can really do.

It was truly astonishing to see how angry all sorts of people were with the behaviour of the News of the World, and how eager they were to do something about it. To the Republic of Twitter, now finding its voice on this subject, it clearly wasn't an ethical minefield, or a thorny legal issue, but a simple case of right and wrong. Morals, as they used to be called. The depths Rupert Murdoch's paper has sunk to – and questions are now being asked about other police investigations, including that into the murder of Holly Wells and Jessica Chapman – is extraordinary.

Democracy, if it is to function properly, requires a free press. A free press holds the government, the judiciary and other public figures to account. The "tax", if you like, for having a free press is the tabloids. And as a concept, they're fine; they're not for me, but then neither is quiche, and I don't need to ban it. But is what's going on here an expression of democracy in action? No, it isn't. Sections of the press now have a far greater influence on government policy than we voters do, and if the hacking revelations are anything to go by they may well have enjoyed a great deal of influence over the police, too. Is that OK by you? What I discovered on Monday night is that it really, really isn't OK by me.

There's a facile argument that says: "The tabloids only behave as they do because people want to read the stuff they print" – as if, in a way, it's our fault. But every business in the land responds to demand from its market; every business in the land needs to make a profit. Most of them, though, manage to stay within the law.