In The Importance of Being Earnest, the prim governess Miss Prism tells her young charge Cecily to omit the chapter on the fall of the rupee in the political economy textbook she has been instructed to study: "It is somewhat too sensational. Even these metallic problems have their melodramatic side." And in Felix Martin's stimulating and timely book we see how right Miss Prism was: money – metallic or paper – may seem deadly dull, but it actually stands centre-stage in today's most important political and economic conflicts. Moreover, it is economists' blinkered insistence that money is just a "technical" and relatively minor issue that explains why they, and their politician followers, brought the world to the brink of catastrophe in 2008 – and why they are conspicuously failing to rescue us from that crisis.

Martin is a member of a small but growing band of heterodox economists who argue that mainstream "neoclassical" economics is seriously flawed. For the neoclassicists, who still dominate university departments, government ministries, the press, banks and international organisations, money is of little interest, dismissed as just a mechanism to make exchange easier – an alternative to barter.

If money is just a lubricant in the engine of the market, then managing money is simple: the market will work best if the value of money remains fixed and stable. And that was precisely the essence of most western macroeconomic policies between the 1980s and 2008: measures designed primarily to stop governments spending, printing and debasing money, and to make central banks the guardians of that totemic fetish – controlling inflation.

But for Martin, Sydney economist Steve Keen and other dissidents, money is more than the oil in the engine – a mechanical lubricant – but a socially-created system of transferable credit, a way of keeping account of what people owe each other, while allowing them to transfer their various "IOUs" to others. Crucially, it is not just governments that create money – others can, too. The recent internet-based Bitcoin is one example; community currencies such as the Brixton and Bristol pounds are others.

But more significant by far is the money created by private banks. Indeed, the recent financial crisis was largely caused by banks issuing IOUs and effectively "creating private money outside the control of government" in a "vast, unregulated 'shadow' banking system". On the eve of the crash, the shadow banks' balance sheet stood at around $25tn in the US alone – more than twice the size of that of the traditional banks.

All of this was largely ignored by mainstream neoclassical economists. For them, these enormous quantities of shadow money simply did not compute. For them, the credit and asset bubbles driven by bank-created money had no major effect on the economy. Here, according to Martin, lies the answer to the Queen's famous charge against the economics profession in 2008: why did none of them see the crisis coming?

Martin dismisses the notion that influential economists were corrupted by close relations with banks and highly paid consultancies – the argument of Charles Ferguson's powerful documentary, Inside Job. For Martin, the problem lies in the realm of ideas, and in part, at least, he is right. Academics – like the priesthoods of old – can generate powerful "groupthink", and fiercely resist whatever challenges their established theologies. But another, more political story can also be derived from this book: the malign influence of neoclassical economics was simply one element of the extreme power – intellectual, political and economic – of international finance, and the weakness of states since the 1980s.

One of Martin's themes is the struggle between states and financiers for control over money, and if anything this crucial issue could have been emphasised more. In 13th- and 14th-century Europe, kings and princes had most of the power, which they abused by debasing the coinage to pay for their wars. But by the late middle ages, the merchants were fighting back. An increasingly international network of financiers had created their own private money – of IOUs or bills of exchange – which allowed them to abandon sovereigns' money altogether. Then, as now, international bankers could trigger a "run on the currency" if they thought governments were spending too much.

This "guerrilla war" between rival moneys continued for some time, but it was resolved, Martin argues, with the creation of the Bank of England in 1694 – a public-private partnership, in which powerful merchants would have a say over the management of the money issued by the state, in exchange for supporting the currency with their loans. This "Great Monetary Settlement" was the foundation of the modern monetary system.

But how was the jointly run money to be managed? Martin has less to say about this part of the story, but the conflict between states and finance continued, though in a different form. In the late 19th century, many governments and merchants agreed on the need to keep money stable by linking it to a rigid gold standard. But as politics became more democratic, the question of how money was to be managed yet again became a divisive political question: should it remain stable in the interests of low-risk trading and lending, as the modern merchants demanded; or could governments print money to invest in economies, help them over downturns, manage productive growth and provide jobs for the mass of the population, albeit at the cost of some inflation?

At the end of the second world war, John Maynard Keynes and the American economist, Harry Dexter White, tried to reconcile the two objectives with the Bretton Woods system, and they were remarkably successful: its combination of a gold-based currency with a flexible state-run system worked for more than 20 years. But a host of crises in the 1970s – American spending on the Vietnam war, oil-price hikes and industrial conflicts – destroyed the consensus that underpinned it.

Yet rather than rebuilding the state-market compromise, an increasingly globalised finance seized the upper hand. States were blamed for the inflation of the 1970s, and international financiers claimed to be the only people who could be trusted to run the global economy. Bankers, like their predecessors in the early modern era, could now punish governments if they thought they were spending too much and printing too much money; as Bill Clinton's strategist James Carville famously complained in 1993, if he was reincarnated, he would like to come back not as the president or the pope, but as the bond market, because "you can intimidate everybody".

However, since 2008, it has become clear that these banks were not the virtuous guardians of monetary purity they claimed to be. They might have been stopping governments from devaluing the currency, but they took advantage of deregulation to print sack-loads of money in the form of IOUs, which funded property and other asset bubbles. The financial crisis showed that these assets had been massively overvalued and the debts could not be paid back. But even so, financiers are insisting that the IOUs be treated at face value. Armed with neoclassical economic arguments, they are fighting against measures that might reduce the debt burden, through either debt forgiveness or inflation. Instead, they insist that government budgets, and the less well-off, should bear the strain through policies of austerity.

Martin convincingly argues that "the current strategy of trying to sweat these debt mountains off over time" is "not politically feasible or economically desirable". But there are no easy solutions. He favours "engineering a few years of significantly higher inflation", or "restructuring the debt burden directly" – that is, writing it off. But many ordinary people will lose from the former, while the latter requires a major rebalancing of the relationship between states and international finance in some new Bretton Woods-style settlement.

There is little evidence that our leaders and their economic advisers have thrown off their intellectual shackles and learnt the lessons of 2008. Until that happens, we can only expect years of sluggish growth and political turmoil. If anything, Miss Prism underestimated the sensational and melodramatic effects of money.

• David Priestland's Merchant, Soldier, Sage is published by Allen Lane