Over three-quarters of people care about the gap between rich and poor but only two-fifths support state action to redistribute from the better off to the less well off. This apparent paradox, from the British Social Attitudes survey, has bedevilled debate about equality on the centre-left. The public shares our concern about inequality, so the argument goes, but are not prepared to support the action necessary to address it. It seems David Cameron really does have his finger on the pulse of public opinion.

But I’m not sure these two findings do represent such a paradox after all. And rather than indicating that the centre-left must abandon its egalitarian ambitions, or pursue them on the quiet, they can give us renewed impetus. This is because they point towards important and neglected arenas of policy. In essence, the concern about inequality is widely shared, but direct redistribution is only one half of the solution. The other, I think, can be described as ‘active equality’.

In ‘Society of equals: a new egalitarian agenda for Labour’, published by Open Left last week, I argue that Labour’s pursuit of equality should embody both sides of this equation. There is an essential role for direct government action to guarantee certain outcomes (like high quality public services) and to redistribute resources (such as to abolish child poverty). Despite all the criticisms, Labour has a record to be proud of on both fronts. Not perfect. Not enough. But not bad at all. And decisively better than what came before.

However, there is a second type of approach that Labour has not paid as much attention to as it might – the consequence of which has been to narrow its policy tools and weaken its political case for equality. ‘Active equality’ is about harnessing the state and constraining the market so as to create the conditions for people to shape the outcomes they seek for themselves and alongside others.

It is inspired by the father of community organising, Saul Alinksy, who stated that: “there can be no darker or devastating tragedy than the death of man’sfaith in himself and his power to direct his future”. Such faith and power are impossible alongside unjustified inequalities, rooted in concentrations of power and structural disadvantages. The purpose of greater equality is the kind of lives it allows people to lead and the kind of society it is likely to foster. Not to compress the income distribution for its own sake.

When it comes to policy, this means addressing the drivers and negative consequences of inequality. This can be done by using the state, markets and society when they empower – and constraining each where they overpower.

So, to make sure people who live and work in the UK pay tax here, we should scrap the anomalous ‘non-dom’ status. To spread power and rewards in the economy we should reform remuneration committees to ensure employees have a voice in setting top pay and promote a diversity of company ownership models, starting with the remutualisation of Northern Rock. In public services, we should challenge selection by house price by widening parental choice and allocating places at oversubscribed schools by ballot. To prevent democracy from being bought, we should limit individual donations to political parties. To encourage a greater spreading of wealth, we should tax the receiver rather than the giver of inheritance.

In short, the goal should be to make society more equal so that people can act together to bring about change. If the ‘rules of the game’ were more democratic and egalitarian, less of the weight would end up resting on the shoulders of redistribution.This would not only be likely to produce more enduring solutions, it would also be morally right.

That’s because it is a demanding and empowering approach. It challenges people to say what they are prepared to do to improve their lives and wider society. And it requires government to share the task of governing with the people. As Alinksy argued: “Self-respect arises only out of the people who play an active role in solving their own crises and who are not helpless, passive, puppet-like recipients of private or public services”.

David Cameron says he wants Britain to be more equal and that he wants to give power to the people. But his hostility to the state, his silence about the market, and his wishful thinking on society means that he chokes off the method for achieving it at source. It is Labour that has the intellectual, organisational and political traditions to create a more equal society. All we have to do is rediscover them.