The European crisis is as much political as economic. It raises fundamental democratic questions. By what right do you govern us? How can we control you while you are in power and how can we remove you if your governance fails? Last week, Michael Ignatieff, former columnist on this newspaper and former leader of the Canadian Liberal party, came to London from a country where politicians can tell the electorate that they have limited powers to remedy their grievances and gazed on Europe with horror. "What," he asked, "is a working stiff in Piraeus meant to make of Christine Lagarde?"

His question answered itself. Madame Lagarde told Greek parents who were scrambling through rubbish tips to find food for their families that she had more sympathy for the children of sub-Saharan Africa. Having unburdened herself of the oafish thought that suffering is a competition in which the poorest can be used as a weapon against the poor, the managing director of the International Monetary Fund added: "I think they should also help themselves collectively. By all paying their tax." The knowledge that she does not pay tax herself in no way restrained her.

The better sort of journalist and, naturally, diplomats are appalled by the Greek charges of hypocrisy that followed. The world has tolerated an over-generous clause in the 1961 Vienna Convention that exempted "diplomatic agents" from tax for more than 60 years. In any case, they added, whether IMF officials and other diplomats pay tax has nothing to do with the eurozone's breakdown. They forgot that perks that no one notices in ordinary times can in crises become as intolerable as the tax exemptions of the aristocrats and clerics were to the French revolutionaries of 1789. In a crisis, the elite has to convince the masses that there is a rough equality of sacrifice – a connection between them and us – or lose legitimacy.

British Conservatives ought to know that by now. If they are defeated at the next election, historians will be able to say that their fall from power began on 21 March 2012, when George Osborne gave the super-rich a tax cut. Tories can argue that allowing the wealthy to keep more of their money will enhance growth, although there is precious little evidence of that to date. They can say that a 50% tax rate encourages tax avoidance and evasion. But whatever they say, no one is listening. By favouring the wealthy, the coalition has gone from being a national government to an alliance of public-school boys that looks after its own. From the moment Osborne finished his budget speech, "we" were no longer "in this together".

"God help me, I can perceive nothing but a certain conspiracy of rich men procuring their own commodities under the name and title of the commonwealth," wrote Thomas More in his Utopia of 1516. Too many voters for ministers' comfort now look at the coalition and see the same.

At least MPs retain the power to pass a motion of no confidence in Osborne. Alternatively, David Cameron can move him from the Treasury or the electorate can throw out the coalition at the next election. Limited democratic action remains possible despite all the constraints globalisation, bond markets and treaties enforce.

In the eurozone, there is no "we" capable of exercising control. The absence of a "demos", of a legitimate political community able to act collectively, explains why the richest, most educated region on the planet is paralysed – to the undisguised amazement of the rest of the world. The walls of the prison in which the eurozone has incarcerated southern Europe and Ireland have been described often enough. National governments can no longer tell central banks to print money to pay off debt. They have no control over interest rates or exchange rates. Their currencies are as fixed as if they were in the gold standard and set at a permanent competitive disadvantage against Germany. Decisions are taken by the IMF, Brussels and Germany rather than sovereign electorates. As we know, power has passed beyond national control.

The European elite's bovine response can still generate incredulity, however. "I can say the medicine is beginning to work," announced José Manuel Barroso, the European Commission president, last month, as youth unemployment in Spain passed 50% and the Greek and Spanish banking systems careered towards a crash.

The EU left attacks Barosso and his kind for his complacency and callousness and every insult they deliver is deserved. But all the left's options come down to Germany, the Netherlands and Finland bailing out the south. Either the north accepts the inflation that will come from the European Central Bank becoming a lender of last resort or the north transfers tax revenues south.

German society is furious. Publishers have rushed out books with self-explanatory titles such as Save Our Money! and The Illegality of the euro-Rescue. The working stiff in Dusseldorf isn't being selfish, or no more selfish than the working stiff in Piraeus who wants his money. He, too, can ask a hard democratic question. How far down the line do north European governments go in giving Brussels budget-making powers before the connection between taxation and representation snaps?

Raoul Ruparel, of the sceptical Open Europe thinktank, told me that if a new European treasury was run by representatives of national governments, it would have democratic legitimacy but would merely reproduce today's impasse between north and south. It could be run by bureaucrats, who could send southern Europe the help it needs. But then it would have no electoral mandate.

Speaking of Utopia, Immanuel Kant imagined in 1795 a world of republics living in perpetual peace. He was not being wholly idealistic. For decades, the European Union fulfilled the prediction of Kant's successors that free, democratic countries could enjoy harmonious co-operation. But the EU has developed into something Kant could not imagine. It is neither a state drawing legitimacy from the loyalty of its citizens nor a free association of sovereign republics, but something in between.

Michael Ignatieff worried that if the lumbering hybrid collapses, nationalist and fascistic forces will once again rise. It's a reasonable fear, as recent European elections show. But I worry more about what will happen if the euro stays and Europeans realise that their elections are shams, their votes count for nothing and the decisions that affect their lives are taken elsewhere.