Courage to put all on an equal footing
So wage inequalities grow and even a Government that redistributes vigorously struggles to keep everybody in the same place.
But there is more. Income inequalities are exceeded by wealth inequalities.
And houses account for 42 per cent of UK wealth, nearly double the proportion in 1971. As we know, house prices have soared, particularly in better-off areas. The differences in wealth between those who own big houses in, say, the south-east and those who rent (and, therefore, have zero housing wealth), or who own sub-standard houses in the northern inner cities, has also soared.
As a recent Shelter report says, this has enormous implications for children. Wealth, in John Major's words, cascades down the generations. (He thought it was a good thing, and wanted more cascading.) To get a decent start in life, many children need their parents' help with meeting the costs of education, training and work experience and with getting a foot on the housing ladder.
Those whose parents hold equity in the housing market are at a great advantage. Shelter suggests our children will soon "be divided more by wealth than has been the case since at least Victorian times" and "for the children of the poor, there will be large parts of the country to which they cannot consider moving, even if they wish to". No wonder social mobility is in decline.
Shelter's figures are alarming. By 2043, it calculates, 10 per cent of children will have recourse to half of all housing wealth, while the 10 per cent from the poorest families will have 0.1 per cent. Though prices may be set to fall now, the difference between houses in desirable areas and those in, say, the inner cities will grow as long as income inequalities grow.
That is a law of economics.
We shall see residential segregation - social and maybe racial ghettoes - on a scale unknown since the 19th century. As a report just before Christmas from the Joseph Rowntree Foundation showed, there are 180 council wards where more than half the children are in families that receive out-of-work means-tested benefits.
I have worse news. House prices, as we know, are boosted by proximity to desirable schools. The latest issue of the Economic Journal quantifies that effect. Where catchment areas exist, access to the "best" as opposed to the "worst" primary schools (as measured by test scores) increases the price of a house by an average of 29 per cent - a bigger effect than its number of bedrooms and almost as big as the size of its plot. As the authors of the research say, we tend to think education and other public goods are provided on an equal basis to all households. In fact, they are often allocated through the housing market.
Paul Cheshire of the London School of Economics and Stephen Sheppard of Williams college, Massachusetts, write that consumption of education "is conditioned on household income in just the same way as consumption of foreign holidays, private education, personal security services or broadband internet access."
School quality is a more elusive entity than this research seems to imply, as test results are influenced by pupils' home backgrounds. But that doesn't change the broad picture: some children are doubly and even trebly disadvantaged and their plight is getting worse.
Government needs imagination, daring and courage if it is to succeed. I hope New Labour can find those qualities in its third term.
Peter Wilby is editor of the New Statesman