The Labour Party has rediscovered equality. Later this month the Fabian Society, the keeper of the party's soul, will publish a revised Clause Four - the symbolic statement of Labour's first principles - in an attempt to embed a commitment to making Britain "a fair and more equal society". This is an ingenious idea. The party ditched its commitment to nationalisation as the prelude to the Blair era. Now, a decade on, the Fabians argue that a Brown era should open with a similar historic rewrite of the party's constitution.

It is as well to be sceptical about Labour's new-found taste for narrowing the gap between rich and poor in society, which has widened under Labour. The government's own target, to abolish child poverty by 2020, looks likely to be missed. But those who have been calling on the party to return to its egalitarian roots should look carefully at the new Clause Four wording: "We believe that no citizen's life chances should be determined by the circumstances into which he or she is born." This is hardly revolutionary and the phrase "life chances" is an ugly one. But deep in the recesses of the Labour Party, something is stirring.

The Fabian Society is an appropriate place for the debate to take place. The original Clause Four was written in 1917 by Sidney Webb, who helped establish that organisation (as well as the London School of Economics and this magazine). In 1992, Tony Blair chose a Fabian Society pamphlet to signal his intention to rewrite the clause, arguing that the party should unite around a shared set of progressive values rather than a commitment to bringing about "the common ownership of the means of production".

The latest proposal on Clause Four comes out of a recent Fabian Commission on Life Chances and Child Poverty, which recognised that while some progress had been made, it was unacceptable that 2.6 million children still lived below the poverty line. Crucially, the commission recognised that far too many people's "life chances" (by which it meant educational attainment, state of health, employment status) are determined by geography and birth. The commission is recommending that equality become the theme of the 2007 Comprehensive Spending Review.

The neosocialists (or new egalitarians as they prefer to call themselves) can be found in some surprising places. In fact, it is getting difficult to move for Labour politicians and wonks pushing theories on how to tackle child poverty or the underachievement of black boys or obesity among children on council estates. Where once Labour politicians raced to show they were business-friendly, now they are keen to show their commitment to the underclass.

Six months ago, during Labour's grim post-election conference in Brighton, I wrote that the party was failing to renew itself. I suggested that new ideas in British politics were coming from the Conservatives and the Liberal Democrats. That is no longer the case. The debate about how best to tackle inequality is everywhere and it is precisely the discussion the party should be having. The seeds were sown last June with the publication of The New Egalitarianism, a collection of essays edited by the Labour insiders Patrick Diamond and Anthony Giddens, extracts of which were published in the NS.

Left-wing critics of the Blairite project should welcome the fact that this debate is taking place not just in Labour think-tanks, but among backbenchers and the wider party. Unlike the lamentable "respect" agenda, this is an issue that could provide a genuine rallying point for the party, although admittedly it has yet to deliver unity between the warring factions. It is telling that the Blairite ultras Stephen Byers and Alan Milburn have used the "E-word" as the pretext for their recent attacks on Gordon Brown, arguing that his position on pensions and tax credits could consolidate inequality.

The Chancellor must be careful not to miss the boat. The Prime Minister is well ahead. He has asked Trevor Phillips, chair of the Commission for Racial Equality, to investigate inequality in Britain. In fact, Downing Street believes this could be the legacy to trump all others. The Chancellor will have to come up with his own vision of egalitarianism soon or people will begin to think he is not an enthusiast.

The biggest danger for Labour is one of definition. By throwing their weight behind the child poverty targets, David Cameron and Oliver Letwin have shown that the aspiration is no longer the monopoly of the Labour Party. The Tory leadership has done Labour a favour by making it difficult for the Conservative Party to criticise redistribution with the old right-wing clichés. Cameron's shift to the left does not encourage prejudice about Labour being the "friend of the benefit scrounger" or the "enemy of enterprise".

But it is now the task of the Labour Party to persuade the public that it has a distinct political programme for making a difference to people's chances of a better life.