The mayor of London demands a law against it to stop tent villages "erupting like boils" across the capital. If you lived like Boris, you too might be a bit paranoid about boils. The prime minister interrupts a trip to Australia to announce that the government is poised to intervene. Meantime, the Church of England is split down the aisle about whether the Christian thing is to embrace the protesters encamped on the doorstep of its cathedral – after all, St Paul was a tent-maker and Christ had a robust approach to moneychangers – or to join forces with the mammonites who run the City of London and have the protest camp evicted. Much of the mainstream media side with the establishment by dismissing them as an incoherent and unrepresentative fringe. Well-paid television interviewers sneer that the protesters are spoilt brats while grand columnists scoff that they will achieve nothing.

Yet they have already done something fairly remarkable. My congratulations to the encampment outside St Paul's for sending almost the entire British establishment into a tizzy every bit as confused as some of the protesters themselves. Amazing what you can achieve by occupying a small, albeit famous, patch of the capital with a few nylon tents and some amateurish banners expressing well-mannered rage about capitalism. You have brought a frown to the forehead of the prime minister, hyperbolic froth to the lips of Boris Johnson, attracted the disdain of a pomposity of pontificators and thrown the state church into something approaching a constitutional crisis. It is twisted knickers time among pundits, politicians and prelates. Imagine what might be achieved if this movement can get really serious and starts taking its protest more directly to the avaricious bankers, corporate larcenists and crony capitalists who are the central source of their discontent with how we live now.

The protest at St Paul's is just one example of an international phenomenon. What began in the Spanish springtime with demonstrations by the splendidly named los indignados has turned viral and global. It is just over a month since the first thousand people turned up at Zuccotti Park in New York to express their rage at Wall Street. Since then, similar movements have come to life in more than 900 cities around the globe. They have camped in front of the European Central Bank in Frankfurt and on the Plaza del Congreso in Buenos Aires.

The default response of establishment opinion is glibly to dismiss these protests as a passing spasm which cannot achieve anything because the movement is either wildly unrealistic in its aspirations for a new world economic order or too vague in its demands. It is true to say that the protests vary in their tactics and are disparate in their goals. Movements like this are often woven from multiple threads of grievance, a tapestry of dissent which can be both a source of initial strength and an ultimate cause of weakness. But they are loosely united by common themes: fury at corporate greed, resentment at lack of economic opportunity, concern about social inequality and alienation from a conventional politics that appears incapable of doing anything serious to address and redress public discontents.

The anarchic end of the protesting spectrum do indeed sound naive when they cry "smash the system", especially when they are either muddled or utopian about what would take its place. More realistic are those protesters who see their role as "raising awareness". That is a very valuable purpose in itself. Simply by existing, they push these issues up the media agenda and towards the front of the public mind. If it makes it just a little bit harder for financial interests and their friends among politicians to put the argument to sleep, it is a little bit worth doing.

The protesters over-claim when they say they speak for "the 99%", but some of their themes do resonate very potently with mainstream voters. The occupation movement is succeeding where conventional politics of both left and right have badly failed. It articulates a profound public resentment with over-mighty finance and the failure of government to do anything about it. The protesters strike a resounding chord when they complain that financial elites are getting rewarded with special treatment while the punishment for their mistakes is meted out on the rest of society.

On top of the billions of taxpayers' money already committed to rescuing the banks, the eurozone leaders have just signed up to providing billions more. Yet from the nabobs of finance there is still not a whisper of a hint of a scintilla of humility or penance. The Institute of International Finance, the main industry organisation, reports that banks are handing more guaranteed bonuses to new employees than they were before the financial crisis. Governments have neither punished those who wrecked the economy nor taken adequate steps to ensure that they will be more accountable and responsible in future. Sir Fred Goodwin – why the hell is he still Sir Fred Goodwin? Three years have elapsed since the bubble burst in 2008 and yet we are still waiting for the fulfilment of promises of systemic reform. The wonder is not that people have been provoked to occupy parks and squares in every continent but Antarctica. The wonder is that this did not happen earlier.

The composition of the demonstrations is interesting. A rough survey of the occupation movement in New York found that about two in three of the protesters are under 34. This is not just because protesting may be more attractive to people with unfurred arteries, but because the young are suffering disproportionately from a crisis not of their making. Youth unemployment in Britain is at record levels: 20% of the under-24s do not have work. In Spain, youth unemployment has surged to a staggering 46%. These protests are an alert to explosive issues of inter-generational unfairness which most politicians have yet to wake up to, probably because their trade is dominated by the middle aged. Their generation often did well enough during prosperity to cushion them from present austerity while the less fortunate young are asked to pay the price.

A big mistake is to think that because the protesters tend to be youthful it follows that they should be treated like children. Richard Chartres, the Bishop of London, has made that error by suggesting to the campers that they ought to leave in return for a debate under the dome of St Paul's – gosh, thanks my Lord Bishop. He further asks them to go on the grounds that: "I am involved in ongoing discussion with City leaders about improving shareholder influence on excessive remuneration."

I am sure that the bishop is well-meaning, but that is not going to cut it. There has been "ongoing discussion" for years. The result, according to the latest report by Incomes Data Services: Britain's top executives gave themselves a 49% increase in their salaries, benefits and bonuses in the past year. It does not even occur to the business and financial elite that it might be good old cynical public relations to moderate their greed while so many of their fellow citizens are suffering the consequences of corporate follies.

Who is truly the more adult: the protesters or an establishment that regards itself as older and wiser? The protesters have largely been very decorously behaved. They have thus far displayed no propensity to riot or to loot. Their tents are erected in rather neat rows. They hold laboriously consensus-seeking meetings at which they keep minutes and take votes. Their spokespeople are polite and articulate. If they do not have all the answers, they are at least posing some of the right questions. I don't see why they should be criticised for the absence of a manifesto when the leaders of Europe spent months quarrelling and flailing over the euro crisis before scrabbling together an expensively botched compromise.

The protesters shun formal leaders and hierarchies – and I also don't see why they should be criticised for this at a time when conventional leaders and hierarchies have been so conspicuously useless. Here are some recent scenes in establishment politics. Silvio Berlusconi displays his incomparable charms by describing Angela Merkel as "culona ichiavabile" ("an unfuckable lard arse"). Rick Perry, contender to become Republican candidate for the great office of president of the United States, questions where Barack Obama was born five months after the White House released his long-form birth certificate, and excuses himself by saying: "It's fun to poke at him." A punch-up breaks out on the floor of the Italian parliament between one right-wing member of the government and an even more right-wing member. Nicolas Sarkozy tells David Cameron to "shut up" because he is "sick" of him. David Cameron elevates the tone at prime minister's questions by shouting: "Complete mug!" at Ed Miliband.

Protesters or leaders? I know who looks the more grown-up.