Two entities are more powerful than any individual government in the West. They are the financial markets and the media. We could argue about the latter, but surely nobody would deny the supreme and often malevolent power of the former.

Yesterday in Brussels a room full of 27 European presidents, chancellors and prime ministers was intent on a single task, trying to do what financial power demands.

We are really talking about the banks. We mean groups such as Barclays Bank, which received 250,000 complaints from its British customers in the first six months of the year. We mean HSBC, which threatened to move its domicile out of London if it didn't get its way over bank regulation. Or Goldman Sachs, the American firm that tried to bully HM Revenue & Customs out of collecting tax that was correctly levied.

How did some banks become "too big to fail"? Why did their reckless behaviour go unchecked for so long and is it restrained even now? How can their directors afford to pay themselves as much as 500 times the average annual salary of those whom they employ? What explains their arrogance? Why don't they get it?

Andrew Haldane, executive director of the Bank of England in charge of "financial stability", in a speech this week reviewing the development of banking over the past 150 years, which is an illuminating exercise if one is to understand today's circumstances, remarked flatly: "For a century, both risks and returns have been high. But while the risks have typically been borne by wider society, the returns have been harvested by bank shareholders and managers." That, actually, is the whole story in two sentences.

It is worth going back to the first half of the 19th century to see banking in its primitive form. Remember its essence is the dangerous task of transforming the short-term deposits you accept, which you must pay back on their due date, into the long-term loans you make, which will sometimes prove irrecoverable. As a result, in those faraway days, the owners of banks often matched the value of their deposits with their own capital on a 50/50 basis to provide a big safety cushion. Nowadays this equity buffer is down to almost nothing.

There was no such thing as limited liability. Bank owners were responsible for paying off every penny of their business's debts. That made them cautious lenders. Of course this system couldn't survive through an industrial revolution with its enormous demands for credit. Banks became limited liability companies in the second half of the nineteenth century. While in retrospect that seems right, it was, nonetheless, a first step in the progressive throwing off of all restraints that has gone on ever since. Recall Northern Rock and its "shadow banking" that eventually drove it into bankruptcy three years ago. That was also throwing off restraint.

Then a century ago, there was a wave of consolidation. This was the time when the chairman of Midland Bank (now part of HSBC) went round England in a taxi buying up smaller banks. We were on our way to the too-big-to-fail syndrome. By the 1930s, as Mr Haldane sums up the situation, "ownership and control were amicably divorced. Ownership was vested in a widely dispersed set of shareholders, unvetted and anonymous. Their upside payoffs remained unlimited, but their downside risks were now capped by limited liability". From now onwards, the banks were to assume greater and greater risk.

At the same time, the banks decided they would take on more debt to boost their returns, thus simultaneously increasing risk and reward. This reached its high water mark in 2007. Now consider an aspect of modern capitalism that we take for granted: that companies can deduct their interest payments from their tax liabilities. The banks were the first to persuade the tax authorities and non-financial firms followed. But looked at in the cold light of day, this is in effect a subsidy for financial risk-taking.

But we are rushing ahead too fast here. The presence of debt amongst a bank's resources ought to have been a restraint, for bondholders generally discriminate between good and bad risks. But by the period between 2002 and 2007, when risk in the system was building strongly, the banks could raise as much new debt finance as they wanted and they all paid much the same for it, good banks and bad banks alike. Why was this? Because the assumption that governments would always bail out the banks had entered into bond investors' calculations. So lend away.

Then, finally, came the crowning folly. Since the late 1990s, banks have set "return on equity" as their target – that is on the highly geared narrow sliver that accounts for only 5 per cent of their resources. They have tied the remuneration arrangements of their directors and senior executives to upward movements in this figure. The result has been to give a mighty boost to risk-taking. In the US, for instance, the typical chief executive of a bank could pocket over $1 million for every 1 per cent increase in the value of his firm. What's not to like?

Well, there is plenty not to like from the point of view of ordinary people. Which means the banks must be ruthlessly reformed. Sir John Vickers's Independent Commission on Banking has proposed that UK banks should have more equity capital and loss-absorbing debt (tick); that their retail banking activities should be structurally separated, by a ring-fence, from their other activities (tick as this would get rid of the too-big-to-fail problem); that banks should have more equity capital (tick) and that a new "strong challenger bank" should be carved out of Lloyds TSB Bank (tick). Tax deductibility for debt should also be removed, as far as banks are concerned, voting rights should be extended to suppliers of debt finance and the return on equity target for executive remuneration should be replaced by return on all capital.