Politicians today are experiencing one of their intermittent bouts of enthusiasm for egalitarian projects. A Tory government has a minister for equality, Boris Johnson is burbling about “levelling up”, while the less ambitious Labour Party is content to pursue its long-established ambition to level down. Social equality is a mirage that has bedazzled Utopians at least as far back as the Levellers and Diggers in the English Civil War. It has been the biggest single cause of mass murder, from the French Revolutionary Terror to the more than one hundred million people slaughtered by Marxism.

Of course governments have a duty to ensure that the poorest of the Queen’s subjects do not fall below a sustainable level of existence, indeed to guarantee that they are raised several degrees above subsistence level and given opportunities to enhance their status through self-help. Where Utopianism errs, however, is in seeking to create a common denominator by lowering the prosperous (which, in the zero-sum thinking of socialists, is desirable, even though it destroys wealth creation, thus impoverishing the whole of society), while promoting the deprived.

Now is not a time to look for clear-headed, objective calculation from our rulers: the fatuous mantra of “equality and diversity” exercises a hypnotic control over boardrooms and universities. On closer analysis, many of those hypocritical, self-interested parties are not pursuing economic equality (the gap between rich and poor has never been wider in Western society), but rather seeking to defend their financial interests by deploying equality for selected minorities as a red herring to deflect attention from inequalities of wealth.

Sometimes, in the world of academe, approaching a question from an unusual angle can deliver extraordinary insights. Ten years ago, an American academic, through painstaking research in what seemed unlikely sources, unearthed some startling information about the phenomenon of inequality. Because his approach was so original as to seem quirky, the media seized upon that aspect of his findings, so that the wider public failed to recognise the significance of a genuinely scholarly investigation. The 120-page research paper he produced would make interesting, if discouraging reading, for today’s aspiring Levellers.

In 2011, Professor Gregory Clark, an economics professor at the University of California, published a study which, in the research based on English data, showed that those bearing names of Norman origin, even today, are around 10 per cent better off than those with historically artisan names and have three years’ more life expectancy. In other words, if your 20-greats-grandfather was called Sir Pagan de Umfraville, even after 950 years, you will still enjoy significant advantages over someone whose 20-greats-grandfather was called Higg, son of Snell.

So, it turns out 1066 and all that had a more permanent effect than a simple dynastic transfer of the throne of England. The Normans were, by any criteria, a most extraordinary people. Starting off as Norse Vikings, they absorbed Frankish manners in their duchy of Normandy and spread their power as far afield as Italy, the Kingdom of Jerusalem and even briefly became emperors of Byzantium (the Courtenay and Brienne families).

At the Norman Conquest of England it was difficult to judge who had the poorer claim to the English throne – William, the bastard son of Duke Robert I of Normandy, or Harold Godwinsson, the Anglo-Saxon usurper of the throne rightfully belonging to Edgar Aetheling. But might proved right and William the Bastard became William the Conqueror. The number of cultural influences that trickled down from the Conquest was incalculable. Although William only sported two lions on his shirt (technically leopards, in heraldic terminology), as is the case with Normandy today, late in the reign of Richard I they were increased to three. So, the proud badge of England footballers today derives from Norman/Angevin royal heraldry.

Anyone who thinks it was all a long time ago and, since the Norman incomers were an elite, rather than a mass migration, its influence must have petered out in centuries past, would have that assumption seriously undermined by Professor Clark’s research, which he expanded into a book in 2014: “The Son Also Rises: Surnames and the History of Social Mobility”.

By researching the subsequent fortunes of families with Norman names such as Baskerville, Darcy, Glanville, Lacy, Mandeville and Venables, in contrast with the continuing lesser social status of those with artisan names such as Smith, Carpenter, Mason, Cooper and Baker, Professor Clark discovered a persistent inequality, to the extent that “Normans” were still significantly over-represented at Oxford and Cambridge today.

There was some narrowing of the gap post-1850, for which he used wills, as the most comprehensive inventory of an individual’s total assets, as a research tool. He found a significant depletion of fertility among the elite from 1900 onwards and a corresponding demographic increase among the descendants of artisans. When it came to the final audit, however, the socio-economic divide persisted.

This does not apply only in Britain. Clark found that social democratic Sweden, despite spreading wealth more equally, had not created significant social mobility. Several supposedly meritocratic Western societies turned out to be no more socially mobile than caste-bound India. In Japan, despite the mass American-supervised social engineering post-War, the old elites retain their position. But the really startling news, for any militant egalitarians tempted to impose radical revolutionary levelling on society, is that even the vast upheaval and slaughter of China’s Cultural Revolution had minimal effect on social mobility.

That strongly suggests social distinctions are endemic and largely immutable in many societies. If Chairman Mao failed to destroy ingrained elites, what price Boris or Keir Starmer? What is the underlying reason? In his early studies, Clark appeared to believe his research proved that nurture, rather than nature, produced social dominance: inheriting estates, wealth, sometimes even titles, created a self-perpetuating ascendancy. Later, however, with an increased evidence base, he seemed to accept there must be a genetic component to inherited elite status, bolstered by his study of social mobility among Ashkenazi Jews.

That debate will run and run. For contemporary Britons, however, the findings that will resonate are that, after almost a millennium, the Normans are still occupying pole position in modern England. They are 10 per cent richer than the descendants of Anglo-Saxon artisans, likely to live on average three years longer, and between 1880 and 2012 the proportion of Norman names admitted to Oxford and Cambridge universities declined by only 6 per cent, leaving them still significantly over-represented today.

So, it appears that when King Harold was killed by an arrow shot into his eye and the old Saxon order perished on Senlac Hill on 14 October, 1066, the resultant change of England’s elite very radically transformed society. Although the Norman influx was demographically modest – the factor that may have made it less resisted by the native population – it was more permanently influential than previous, larger migrations.

Tennyson may have found it comforting, in his poem “Lady Clara Vere de Vere”, to claim “Kind hearts are more than coronets/And simple faith than Norman blood”, but the persistence of at least a muted element of Norman ascendancy after 27 generations suggests that social mobility is a less practical ambition than is frequently assumed and that Boris Johnson may face a daunting task in levelling up. However, he may succeed, considering he has a family heritage of indomitable governance, since Boris is the 29-greats-grandson of William the Conqueror. Noblesse oblige.