Look out for 'the British Dream' - soon to be playing in an election campaign near you

Whether you are a Blairite or a Brownite, the goal for a third term will be to deepen progress towards social justice

Two PhD students meet in the refectory. "What's your doctorate in?" asks one. "How the American class system works," replies the other. "I didn't know there was a class system in America," says the first. "That's how it works," says the second. An old joke that still contains an important truth.

One of the most attractive features of the US is the near universal belief that anyone can make it to the top however lowly their origins. We Old Worlders can see that it's just a myth, because we are not so naive, and we know that the US is a more unequal society than any European country. What we are less ready to admit is that America is also a more mobile society than Europe.

The American Dream is not purely the figment of false consciousness. The gap between rich and poor in the US may be great, but the chances of jumping across it are greater than in most other countries. That is why it was so intriguing to see Alan Milburn, Labour's election supremo, devote his first big speech since his return to Cabinet to the subject of social mobility. The American Dream is one of the most powerful themes in American politics. One of John Kerry's many weaknesses was that he did not embody it in his privileged life story. Nor did George Bush of the hereditary presidency but it ought to be easier for a Democrat to mobilise its power than a Republican. Indeed, it was Bill Clinton, who came from a troubled childhood in a place called Hope, who gave it its most authentic recent expression.

British politicians have fitfully and not too convincingly tried out the sound bite of "the British Dream" in the past. One of them was Tony Blair, in an interview with the Daily Mirror when he was leader of the opposition. Nothing has been heard from him on the subject since. Another was Michael Howard, soon after he became leader of the opposition, in a speech last February. With some cheek he cited the fact that Britain now "boasts" black Cabinet ministers as evidence that the highest places were now open to people of all backgrounds. So they are, thanks to a Labour Government. But Milburn's speech on Tuesday was, at last, a serious attempt to get beneath the sound bite and answer some big questions of social policy.

This is encouraging, when so much of politics seems to be about personalities and short-term positioning, not least Milburn's own return to the Cabinet, which was all about the Prime Minister's attempt to prevent all power in his Government being sucked into the Treasury by the dense star of intensely compressed matter known as Gordon Brown. Milburn's speech is a reminder that, even in the midst of the fiercest clash of personal ambitions, politics is about real choices that matter. Whether you are a Blairite or a Brownite, the question for the third term will be how to deepen and entrench the progress towards social justice that has been made over the past eight years.

What was striking about Milburn's speech was the extent to which he seemed to concede the critique shared by many Brownites of the Government's failure to do more to shift the deep trends towards greater equality. Over his lifetime, he said, "social mobility has slowed down when it ought to be speeding up".

He took as his text research carried out at the London School of Economics that suggests people's chances in life are more determined by their parents' status than ever before. He should be careful, I think, not to give too much credibility to those gloom-mongers who say Blair is just a Tory, that the rich are still getting richer and the poor getting poorer. But he is quite right to accept that all the good work this Government has done, especially in lifting children out of poverty, needs to go much further if declining social mobility is to be reversed.

There is some coming together of Blairites and Brownites in the struggles over Labour's manifesto. Brown and his supporters have worried about social mobility as a political issue for some time. Both sides are using Brown's phrase, about trying to build a "progressive consensus" in Britain so that the gains of Labour's long period in government cannot be swiftly rolled back whenever the Conservatives or a Liberal-Conservative coalition get in. But there are sharp differences about what that requires.

Milburn's stress on asset and home ownership cuts against the grain of what many of his supporters assume Brown's priorities to be. It is true that Brown was behind the child trust fund scheme that will, next April, hand out a lump sum of up to £500 to every child born in the past two years, a rather cynically-timed step towards what Milburn called "an asset-owning democracy". But some Brownites are likely to resist Milburn's call for a "wider policy effort to make Labour the modern party of home ownership".

The revival of social housing has become something of a religion in large parts of the Labour maquis that is working against Blairism from within. Yet the implication of any genuine attempt to promote social mobility should be to move people out of social housing into home ownership wherever possible. As Milburn noted, "the housing market is making inequality wider and further impeding social mobility", but the reaction to that should not be to try to roll back Thatcherism but to extend it even further. So far, though, John Prescott shows no sign of extending the right to buy from council tenants to those of housing associations - despite evidence from some MPs that their constituents will wait long periods in overcrowded conditions for a council house which they can then buy, turning down offers of housing association homes which they cannot.

There are many other gritty issues like this, including getting people off incapacity benefit and into work, getting other people off tax credits and into higher-paid work and the extent to which the state should be trying to bring up everyone's children. But at least there is some creative thinking going on at the highest levels of the Government about fighting the election on something more than Labour spending versus Tory cuts.

I'm told the Prime Minister has said to his campaign team that he is convinced the system is already "bumping up against the limits" of higher taxes. That means more emphasis not just on reform of public services but on the state acting as a facilitator for people taking responsibility for their own life chances. Students paying more towards the cost of degrees that increase their earning power, for example.

There is still a great tension at the heart of Government between those instinctively drawn to market solutions and those who look to other motives of human action. Gordon Brown has recently played down his free-market credentials, but social mobility is a clever way of tying him into a common approach for the election. Not only is he knowledgeable about the technical issues, but he has a feel for American politics and the political power of the promise that everyone should have the most equal chance possible to make the best of themselves, regardless of where they start in life. Expect to hear a lot more about "the British Dream" over the next six months.

j.rentoul@independent.co.uk

The writer is chief political commentator for 'The Independent on Sunday'