This is (most of) the concluding paragraph of Geoff Payne’s The New Social Mobility, and it warrants drawing to people’s attention:
The problem is that policies that would work quickly and powerfully are politically unpalatable. Resistance to reforms aiming to improve gender equality in pay and employment, especially in the higher reaches of companies, provides a solid example of how this works. Abolition of public and selective schools; imposition of class intake quotas on Russell Group universities; progressive taxation (on inheritance, property values and very high incomes), regional redistribution of expenditure and specific benefits for those in poverty and poor-quality jobs would shake up British mobility. Such policies may be those most often embraced by the Left, but the fundamental truth that needs to be faced is that those with advantages must give up some of them to make space for those who start off with disadvantages. If we really want more mobility, improving equality of ‘opportunity’ is a red herring – what matters is improving equality of ‘outcome’. Improving mobility rates will do little to reduce social inequality, but reducing social inequality is the sure way to achieve greater social mobility.’