All the Labour leadership candidates who were part of the last government distance themselves to some degree from the past. But it is not enough to "move on", as David Miliband puts it, as if the consequences of the past are not still with us.

New Labour's past consolidated a system in which money is more powerful than votes. It is this that enables Cameron et al to move so quickly to try, finally, to destroy the welfare state.

The only candidate worthy of election is one who can be a voice for a politics that aims to put democracy in control of markets: that is, a party leader unlike any we have seen before, a politician who acts as one voice supporting a movement of many voices, coming mainly from outside the political class.

Here we might take off the shelves Parliamentary Socialism, the classic book on Labour by the late Ralph Miliband, David and Ed's father. Miliband Sr analysed how Labour's deep attachment to parliament, and the British state, overrides episodic and largely rhetorical commitments to socialist change. As he put it, "Of political parties claiming to be socialist, the Labour party has always been one of the most dogmatic – not about socialism, but about the parliamentary system".

At first, Ralph Miliband left open the possibility of transforming Labour into a party able to lead a process of socialist change. But, observing the 1964-70 government, he concluded that the DNA of the British state – its deference to the financial interests of the City and to the primacy of the US in foreign policy – had become part of Labour's DNA, too.

This did not, for him, mean the end of the Labour party for socialist politics. His analysis of the party's history, in particular its relationship with the unions, meant he understood that large numbers of socialists were active in it as the only means of working-class political expression. He also recognised that the mass of working-class people were not socialist, so they were not "betrayed" by the party's leadership. The main defect of that leadership, in his view, was how little it contributed to helping people understand the relevance of socialist policies to their needs.

He drew three complementary conclusions. First, in contrast to the left's endless wrangles over whether to work inside or outside the Labour party, he argued for socialists in and out to collaborate closely. At the same time, he argued a new party was needed to challenge Labour from the left. It would, though, be the result of processes that the left could only in part control, including changing the electoral system.What was needed in the meantime was persistent consciousness-raising. He talked frequently about making socialism the "common sense of the age".

For most of the 20th century, socialists remained active in the Labour party: it had more or less democratic policymaking structures, along with an explicit commitment to socialising the means of production (the original clause IV). Yet today, these structures have been not so much (necessarily) updated as replaced by weak consultations and vague pledges to fairness and opportunity amid a culture hostile to debate. This culture is responsible for the intellectually exhausted party we see now.

Its would-be leaders may court votes by referring to "this great party" but in many localities, under New Labour, it has become a rump. Miliband Sr predicted such a dynamic when he referred to "the kind of slow but sure decline which – deservedly – affects parties that have ceased to serve any distinctive political purpose".

Before the decline becomes terminal, there is a pressing purpose that what is left of Labour could make its own. A defining issue for the coming years will be the defence of public services. This has significant strategic implications. Most TUC-affiliated unions are now public sector unions, but a majority of these are not affiliated to the Labour party.

So, defending public services will require all those broadly on the left to collaborate across party divides. The need presents itself more acutely than ever it did in Ralph Miliband's lifetime, to create a non-electoral political force, oriented not at Westminster but within local communities and workplaces. And it must make common cause with the international networks of unions and citizens' movements that already have had some success – for instance, in reversing the privatisation of water.

Ed Miliband talks of "renewing the movement". Movements are never in abstract. What better way than to declare that New Labour's embrace of marketisation was, quite simply, wrong? He could use his high profile to assert in modern terms the case for public goods in a dominant culture where commodities are all that matters. By supporting practical alternatives to privatisation, he could hold out the model of a participatory state, against Cameron's "big society" – aka the dismantling of the state.

This presents Ed with a challenge: to break from the parliamentarism his father so rigorously anatomised and be not so much a traditional party leader as one distinctive, powerful voice in a movement made up of many. It's the only way genuinely to move on.