When we talk about social inequality in Britain we are often reluctant to look too directly at certain issues. Politicians are understandably uncomfortable about talking about the fact that, while seven per cent of UK pupils attend private schools, those children go on to make up 36 per cent of the cabinet and 55 per cent of all civil servants.

We are reluctant to acknowledge such entrenched privilege, or to look at the fact that, to have a more equal society, sometimes the better off, or their children, may have to give up some of their advantages. The report by the Coalition Government's Social Mobility Commission claims parenting advice is the last remaining taboo of government policy. It says politicians and teachers have been wary of "calling out" poor parenting and argues that bad parenting is perhaps the most important factor determining people's poor life chances.

There is certainly a case for offering more help and advice for parents. The decline of the nuclear family and the fact that families are often more widely dispersed than previous generations has removed some of the standard pillars of support and ways in which parents get advice and ideas.

But there are other factors that contribute to inequality in the UK. Primarily, there is child poverty: growing up in poverty, regardless of the quality of your parenting, has the biggest impact on social mobility.

Poorer children struggle more from the start. They may lack books, or a quiet place at home to work; they may go to school hungry, or with other worries that impair learning.

The previous Labour government, regardless of its failings, made a determined assault on child poverty and appeared to be making progress. In coalition, David Cameron has called definitions of child poverty into doubt yet has stalled on any alternative, while the Liberal Democrats have wrung their hands on the sidelines.

As social mobility tsar, Alan Milburn points out that we have too many dead-end, low-paid jobs, with five million people working for less than a living wage. There are other good ideas in Mr Milburn's report. Higher pay to encourage the best teachers to work in poor areas or challenging schools is worthwhile. The Scottish Government could look at such a policy.

Meanwhile, the commission suggests unpaid internships should be banned. If the Scottish Government gains powers over the DWP's Work Programme, this could happen. At present, it is hard to see a government that encourages job-seekers to work for free legislating to ban other employers from adopting the tactic.

There is increasing evidence that more equal societies are healthier societies on a range of measures. As the report argues, it makes the UK weaker, and our institutions less informed and less effective than they could be. The Coalition Government has presided over rising in-work poverty, food banks and has done little to tackle entrenched elitism. The commission's report is sound. But parenting advice, while worthwhile, is ultimately just a distraction while the Government pays lip service to social mobility.