On Saturday Birmingham city centre was shut down because the English Defence League were in town, marching, chanting, and doing quite a lot of drinking. The unsuspecting city visited by a rag-tag of thugs and football hooligans bent on disturbing the peace has become part of the antisocial calendar.

But to dismiss the group as modern blackshirts is a mistake. In fact, the EDL is more accurately described as a Facebook group with a militant wing. Behind the 500 or so that hit the streets this weekend exists a much larger, highly motivated online community of thousands of sympathisers and supporters who set the mood music, recruit, proselytise and organise. Like every group founded in the Facebook era – UK Uncut being one example – social media is written into its DNA.

To understand the EDL requires looking past the militant wing and peering into its online world, because that is where most of the action is. The heartbeat of the movement is its Facebook group, with its 30,000 or so fans. Not content with colonising our social lives, Facebook is also transforming our political ones. It has flipped the notion of group membership on its head, because the barriers to entry are so low. Whereas the British National Party maintains exclusivity through formal lists and subscription fees, the EDL is the opposite: click "like" and you're in. For the group's leaders, this skittish self-selection membership scheme means more numbers to bully people with, but less control over what your supporters say or do. This includes filling in an online survey – including one from Demos, which well over 1,000 did.

Our report – Inside the EDL – shows quite a different picture from the one we're accustomed to. EDL supporters are actually a mixed bunch, ranging from the committed peaceful democrat demanding that gay people be spared the horrors of sharia law courts all the way, it is alleged, to Anders Breivik, the Norwegian terrorist who murdered 77 people in July. Sometimes, this means supporters betray the official party line. Although BNP members are not formally welcomed into the EDL, one third of its supporters voted for them at the last election. But equally, the racist vitriol found in its chaotic online chatrooms or chanted at demonstrations obscure more thoughtful and moderate elements. Overall, what defines them is not a violent hatred towards all Muslims – though that exists – but pessimism about the UK's future and worries about immigration and high levels of joblessness. This is tied together with a pride in Britain, British history and values, which they see as being under attack from Islam. (Hardly surprising when much of the rightwing press reports that they are.) Their frustration at an out-of-touch, spineless liberal elite is palpable. While some find the chance of a Saturday afternoon punch-up too good to miss, the majority disavow violence.

The EDL's melange of virtual and real activism is characteristic of the way millions of young people now relate to politics. It shares organisational genes – and admittedly little else – with the OccupyLSX movement camped outside St Paul's Cathedral. This nascent, messy and more ephemeral form of protest perplexes the security services because no one knows whether people in the real world do what they threaten in the digital one. Although they have collected social media data since the 2009 G20 summit, the police were left floundering and "overwhelmed", as they put it, by "the chitter chatter" of the student demonstrations and the London riots. Faced with an ocean of conversation threads, idle threats and anonymous bravado, they were unable to separate the significant from the irrelevant.

Reading the social media buzz in the build-up to the weekend's demonstration, one might have reasonably concluded that thousands were about to descend on the Midlands. In the event, there were fewer than 500. This is because, far from being an enormous mobile street army, the overwhelming majority of the EDL's Facebook fans are actually not that active at all. Around a quarter are "trolls" (internet slang for an infiltrator intent on sowing discord), spies, police officers, the vaguely curious and probably a few journalists. Of those that remain, only a quarter have travelled any distance for a national demonstration – the stuff we associate with them – while almost as many spend time leafleting, flash-mobbing at local landmarks, and even issuing legal challenges (often against mosques).

Most are keyboard warriors who limit themselves to sharing web links to stories and generally whipping themselves into a state of digital apoplexy. This is why, despite the noise and numbers, the group never mobilises more than a couple of thousand people – a scary sight if they advance on your town, but hardly sufficient to shake the nation.

Online activism – "clicktivism" – is a powerful agent of change, and we still do not know how powerful. The EDL, at least for now, remains mostly online. That is probably for the best. But it is worth trying to understand and respond to some of the concerns of this small army of virtual supporters, because that could easily change.