Much of the upper crust of British society is a racket for the privileged in defiance of the democratic wishes of the majority. That really is the core of Elitist Britain, that while 95% of Britons believe "in a fair society every person should have an equal opportunity to get ahead", the figures in a government report published on Thursday reveal an ingrained unfairness.

Only 7% in Britain are privately educated, and yet this section of society makes up 71% of senior judges, 62% of the senior armed forces and 55% of permanent secretaries. It is quite something when the "cabinet of millionaires" is one of the less unrepresentative pillars of power, with 36% hailing from private schools.

The statistics should provoke Britain's media into a prolonged period of self-reflection. They probably won't since 54% of the top 100 media professionals went to private schools, and just 16% attended a comprehensive school – in a country where 88% attend non-selective state schools. Forty-three percent of newspaper columnists had parents rich enough to send them to fee-paying schools.

In the case of the media this has much to do with the decline of the local newspapers that offered a way in for the aspiring journalist with a non-gilded background; the growing importance of costly post-graduate qualifications that are beyond the bank accounts of most; and the explosion of unpaid internships, which discriminate on the basis of whether you are prosperous enough to work for free, rather than whether you are talented.

Why does the unfairness highlighted by the report matter? As it points out, elitism leaves "leading institutions less informed, less representative and, ultimately, less credible than they should be", meaning they focus "on issues that are of salience only to a minority but not the majority in society". If there are so few journalists and politicians who have experienced, say, low wages or a struggle for affordable home, then the media and political elite will be less likely to deal with these issues adequately. Instead, they will reflect the prejudices, assumptions and experiences of the uber-privileged.

The flaw with the report is an implicit assumption that inequality is not the problem, but rather that our current inequality is not a fair distribution of talents. "If only a few bright sparks from humble backgrounds could be scraped into the higher echelons," seems to be the plea.

Certainly Britain is in desperate need of radical measures to ensure all can realise their aspirations, including the banning of unpaid internships, the scrapping of charitable status for private schools, investment in early-years education, and dealing with issues such as overcrowded homes that stifle educational attainment. But surely Britain's chronically unequal distribution of wealth and power has to be tackled too.