You don't have to love anarchists or even like them to give credit where it's due – their spectral attendance in the political arena guarantees entertaining fright. Their pageantry and occasional wit is a positive caution. And for sure they have been keeping the flame of direct action alight while other movements have been slow to do what movements are supposed to do – move.

But their contribution to the protests radiating across Europe – and yet to ignite our becalmed islands – is less significant that you might think from the panicky preparations for the G20 summit.

Bossnappings are not sprung by hooded urban guerrillas; egg-throwing at executives is not the work of cuddly crusties. The demonstrations against mass youth unemployment rustling through Greece may enjoy their support, but they are a mass movement of many origins.

Executives have been kept at work, forced to keep the company of colleagues they're trying to dump, by French trade unions refusing to take no for an answer. Executives have been left with egg on their face by Spanish workers, likewise enraged that only the workers are paying the debts of casino capitalism. These European trade unions are relaxed about reminding everyone that the executives "who sow misery reap fury".

There isn't a wave of anarchy flooding Europe. But anarchism – a long and sometimes honourable – component of European radicalism is being encouraged by no less than Tory journalist Max Hastings whose normal hauteur has been broken by a splenetic outburst against Sir Fred Goodwin and the "robber bankers" who, he says, should get their windows broken until they wise up to the way we feel. He exhorts us to "get the boot in and keep kicking".

Perhaps Hastings's violence is so intense because the posse responsible for this crisis number among his cohorts, he knows them, his party emancipated them, and he is taking it personally.

That's why we should beware the "law and order" rhetoric that is beckoning the G20 protests. Invoking the threat of anarchists is to misread the zeitgeist signified by Hastings's call to arms – or rather, feet.

For the first time since the protest against the war on Iraq, an extraordinary national consensus is finding voice. And for the first time in a generation, the TUC is mobilising. Uniquely, it is organising a political partnership for the 28 March demonstration that stretches from Oxfam to the Salvation Army, from green to grey power.

There is a silence from its son and heir, the Labour party, because, of course, its leadership is shamelessly culpable.

But we need to beware not only the police but ourselves – the anarchists among us are estranged from the institutions; that is their ideology and their modus vivendi. The rest of us, from trade unionists and non-governmental organisations, to reds, greens and blues probably agree with TUC general secretary Brendan Barber that we need to rise to the time, intellectually and ideologically, to produce a fairer and greener world out of this crisis.

He's right. The trade unions need to become assertive in the strongest sense – though diminished they are still a mass membership movement, they need to escape from their craven subordination to a government that needs their money but derides their influence. They need to translate their institutional presence into power.

And for the first time in their history, they need to use their institutional expertise to check out what "fairer, greener globalisation" might mean and to help make it so: by transcending their own borders, by abandoning the short-term, anti-green calculations that have often made trade unions enemies of the environment, and the traditional sexism that made them enemies of equality.

Now is the time for a new social contract – not just the kind of deal negotiated between Labour and the unions in 1974 (interesting and innovative though it was) but a historic approach fashioned from a scale of networking, imagination and intervention that we've not had in Britain in living memory. So, the question is not – as we might have mused a couple of years ago – if, or when, but how, now?