After his spokesman's brusque dismissal of John Major's comments on social mobility earlier this week ("what counts is not where you come from but where you are going," was the non sequitur offered), David Cameron has issued a lengthier response to the former PM's fusillade. He told reporters on the first evening of his trip to India:

You only have to look at the make-up of the high levels of parliament, the judiciary, the army, the media. It's not as diverse; there's not as much social mobility as there needs to be...I agree with [Major] that we need a far more socially mobile country. That is something we need to do far more about … We are making some progress but it's not fast enough and we need to go further and faster. What I want to see is a more socially mobile Britain. I want to see a Britain where no matter where you come from, what god you worship, the colour of your skin, what community you belong to, you can get to the top in television, the judiciary, armed services, politics, newspapers. A lot of these areas are important.

Few will disagree with that, but read the latest comments made by Alan Milburn, the former Labour cabinet minister and the government's adviser on social mobility, and it becomes clear how little Cameron has engaged with the problem. Milburn rightly noted that "deep-rooted inequality and flatlining mobility have been decades in the making" and that "in most developed countries there has been a declining share of economic growth going to labour (and a higher share to capital) at the same time as there has been growing wage inequality. In the UK, the share of national income going to wages of workers in the bottom half of the earnings distribution decreased by a quarter between 1979 and 2009."

The UK's stagnant and even declining social mobility owes much to the surge in inequality that took place after 1979 (the gini coefficient rose from 12.9 in 1978 to 22.2 in 1990), which Labour, to its shame, failed to halt. As the graph below from the empirical masterpiece The Spirit Level shows, it is the most unequal countries, such as the UK and the US, that have the lowest levels of social mobility, while the most equal, such as Sweden, Canada and Japan, that have the highest.

This is hardly surprising: it's harder to climb the ladder when the rungs are further apart. As Will Hutton's report on public sector pay for the coalition noted: "There is now good evidence that income inequality can become entrenched across generations, as elites monopolise top jobs regardless of their talent, gaining preferential access to capital and opportunities. This harms social mobility."

There was a time when Cameron was prepared to draw on such insights. In his 2009 Hugo Young Memorial Lecture, he noted:

Research by Richard Wilkson and Katie Pickett has shown that among the richest countries, it's the more unequal ones that do worse according to almost every quality of life indicator. In "The Spirit Level", they show that per capita GDP is much less significant for a country's life expectancy, crime levels, literacy and health than the size of the gap between the richest and poorest in the population. So the best indicator of a country's rank on these measures of general well-being is not the difference in wealth between them, but the difference in wealth within them.

But he has since resorted to Thatcherite type, treating the size of the gap between the rich and the poor as an irrelevance and offering only a more elegant version of Norman Tebbit's "get on your bike". "You’ve got to get out there and find people, win them over, get them to raise aspirations and get them to think that they can get all the way to the top," he said last night.

Some coalition ministers have recently pointed to data showing that inequality fell to its lowest level since 1986 in 2011/12 as evidence that the coalition is widening opportunity even at a time of austerity. But this is not as surprising as they suggest; it's normal in times of economic stagnation for inequality to fall as middle class earnings decline and the automatic stabilisers maintain the incomes of the poorest. The decision of high earners to defer earnings until 2012/13 in order to benefit from the cut in the top rate of tax is also likely to be a factor. But it's still a finding the Tories hail as they seek to prove that "we're all in this together".

They would be wise, however, to resist the temptation to do so. Owing to the coalition's welfare cuts, many of which only took effect this year, inequality is forecast to significantly increase between now and 2015-16. In particular, George Osborne's decision to cap benefit increases at 1 per cent for at least three years (an unprecedented real-terms cut) means the poorest will see a sharp fall in their incomes. The IFS expects inequality "to rise again from 2011–12, almost (but not quite) reaching its pre-recession level by 2015–16." While the Tories can take little credit for the fall in inequality (which is largely due the decline in real earnings), they will deserve the blame for the rise.

Cameron's refusal to even acknowledge this problem, and its implications for social mobility, shows how far he is from living up to his rhetoric of spreading opportunity.