It is usually a good idea in politics to fight the opponent you have, rather than the one you want. Ed Miliband would like David Cameron to be an uncaring, capitalist zealot, intensely relaxed about poverty and inequality. Yet the Prime Minister confounds the Labour leader by refusing to play along.

On 2 November last year, for example, Miliband challenged Cameron in parliament to do something about the growing gap between exorbitant executive pay and the meagre wages of ordinary workers. The attack was meant to probe the Prime Minister's discomfort over an article by the Archbishop of Canterbury, published in that morning's Financial Times, bemoaning the unfair allocation of profit and pain after the banking crisis. Cameron stunned Miliband by agreeing with the Archbishop, adding: "It is unacceptable in a time of difficulty when people at the top of our society are not showing signs of responsibility."

The Labour leader later told friends that the exchange proved the Prime Minister's capacity for "breathtaking opportunism". Miliband's breath might not have been taken so easily had he paid closer attention to what Cameron said in opposition. There were clues. In a speech to the World Economic Forum in Davos in January 2009, the Tory leader fretted about a system in which, "too often, the winners have taken it all". He called for "capitalism with a conscience", which would entail abandoning "old orthodoxies" and discarding "old rules".

Reward and opportunity

Those would be the same rotten rules that Miliband declared himself uniquely qualified to rip up at his party conference last September. A plea for more "responsible capitalism" is meant to be the unifying theme in the Labour leader's bid for the nation's affection. First, however, he has to win the nation's attention, which is made harder in a field that has suddenly become crowded. On 19 January, Cam­eron made a speech revisiting the theme of morality and markets. On 16 January, Nick Clegg had a go, calling for "redistribution of power" in the economy.

There is now a consensus that something has gone systemically wrong with the way in which British society parcels out reward and opportunity. The race is on to be the party most conspicuously determined to do something about it. For Lib Dems, this is a battle for survival. They are known for all the wrong things: loving the European Union; a failed bid to change the voting system; breaking promises on tuition fees. Clegg badly needs some popular device to distinguish his party as the conscientious voice within the coalition. He is determined to take possession of the "responsible capitalism" agenda, presenting it, somewhat fancifully, as part of a Liberal tradition stretching back to William Gladstone and John Stuart Mill.

The Tories, meanwhile, have no intention of surrendering such a prime patch of policy turf. Opinion polls show that the Conservatives are still perceived as unduly sympathetic to the rich. Concern is growing at the top of the party that persistent headlines about bonuses and executive pay are eroding support for the government's austerity programme. "There is a remarkable degree of acquiescence," says a cabinet minister. "The one gap is the sense that those at the top are not playing their part." That has persuaded George Osborne to pitch the Tories as eager scourges of cronyism and greed. "It doesn't come naturally," says a cabinet colleague. "But he recognises that this is a key test in people's minds of how the party is seen."

The Prime Minister, by contrast, has a record of expressing uneasiness about the ugly side effects of an unbridled market economy. There are speeches dating back to the early years of opposition on poverty, social cohesion, corporate responsibility. Those interventions, casually dismissed by Labour as glib marketing exercises, are now being excavated from the Cameroon archive. Downing Street aides brandish them as evidence that the Conservative leader was talking about responsible capitalism when Miliband was still serving Gordon Brown, the man who many voters blame for letting the bankers off the leash.

The Labour leader has responded to this land grab with self-assuredness, touching on complacency. He expects the country to utter a mass snort of derision when Cameron says he wants to reform capitalism. "The public are not going to buy it," Miliband told the Guardian on 6 January. This confidence rests on the belief that Labour is the only party with sufficient depth of social conscience to talk credibly about injustice. Miliband's view is that only Labour can be trusted to administer austerity without wanton cruelty. As he said on 10 January: "Only Labour can deliver fairness when there is less money around."

Picking pockets

There are three problems with this approach. First, it implies a rebuke to those who voted for other parties. Second, it glosses over the party's patchy record on delivering fairness when there was plenty of money around. Third, most people dislike politicians equally and are unmoved by nostalgia for party tradition. There is hardly a less persuasive argument on responsible capitalism than the one that goes: "That lot say they want it because they are cynical opportunists; we say it because we have nobility of purpose inscribed in our souls."

There are many reasons why Cameron and Clegg might fail to build a fairer economy: the cuts, rising unemployment, the absence of growth. The circumstances promise to raise inequality and stifle opportunity faster than the coalition can imagine ways to offer redress.

Miliband believes that the obstacle is more fundamental, however. He thinks that the Lib Dems and Conservatives are prevented by ideological blinkers from seeing the true scale of the task; he supposes them unequal to the historical moment.

Yet, as Miliband's eyes are set on a far horizon where he thinks he can discern voters realising that the duty to fix the British economy belongs inevitably to Labour, Clegg and Cameron are going through his pockets for slogans and policies. The Labour leader is fond of saying that his opponents "just don't get it". When it comes to capitalism, it would be safer to assume that they do.