I grew up in Oxford, but left my hometown to study and then worked at universities in Newcastle, Bristol, Leeds and Sheffield. People who read my words but didn't hear my accent often assumed I was from the north. But now I've come full circle, and have taken up a chair in geography at Oxford University.

It is geography that reveals just how divided we have become as a society in this country. There are places from which it appears almost impossible to succeed educationally and others where it seems very hard to fail. On any given day, a fifth of children in Britain qualify for free school meals. Just one in 100 of those children get to go to either Oxford or Cambridge University. Four private schools and one highly selective state sixth-form college send more children to Oxbridge than do 2,000 other secondary schools. The most prestigious 100 schools secure 30% of all Oxbridge places. And 84 of them are private schools.

People often complain that the national debate on higher education is unfairly dominated by interest in entry to these two universities. But it matters. The richest 1% (people with a pre-tax household income of at least £160,000) dominate decision-making in this country. How they behave is a weathervane for social mobility in Britain.

Income inequality has now reached a new maximum and, for the first time in a century, even those just below the richest 1% are beginning to suffer, to see their disposable income drop. When you exclude the top 1%, income inequality within the rest of the population, within the 99%, is now lower than at any time since Margaret Thatcher was prime minister. Or, as put in economist-speak by the Institute for Fiscal Studies last year: "Over the past two decades … inequality among the bottom 99% has fallen: the Gini coefficient for the bottom 99% was 5% lower in 2011–12, at 0.30, than in 1991."

We now know that economic inequality changes how we think and is linked to biases in self-perception. When university students from 16 countries around the globe were asked to rate how they individually compared to other students in terms of the big five personality traits (agreeableness, conscientiousness, extroversion, open-mindedness and emotionality) it was those in the more economically unequal countries, such as the US, who were most likely to frequently say that they were superior to their peers. Fortunately, perhaps, the UK was not included in that particular study. When it is, we may find that we are not as self-deprecating when tested in private as we are in public.

Being more prone to be elitist and trumpet our own talents, both actual and imagined, is not necessarily unwise in a more unequal society. In such a society, to prosper may well require individuals to be more upbeat about their individual abilities, to think they are better than others. How else do you justify your position if you are paid much more than the average in a very inequitable society?

However, the tendency to self-aggrandisement has many downsides. As acclaimed author, academic and working-class child Marshall Berman said of his student days: "The experience of studying at Columbia, Oxford and Harvard was intellectually exciting but socially lonely. They all catered to the rich, to the current and wannabe ruling class, and I felt I didn't fit in." When clever upstarts get into the ranks of the super-paid they often find they do not fit in easily there, just as highly paid women often also discover.

Today in education the thinking and attitudes of a few of our elite have come to be presented as common sense. Some of the members of the 1% like to portray state schools as the problem, and they suggest that those schools are the reason why others are paid so little and why incomes have dropped. To be able to do this they sometimes suggest that there was once a golden age of state schooling when the grammar schools gave working-class children a chance. Some may believe this was true, but grammar schools were a relic of an older, even more unequal age. Some of the new top 1% would prefer to see the privatisation of all schools.

It is almost 20 years since Milton Friedman explained to the Washington Post how state education could be privatised in the US. He said: "I believe that the only way to make a major improvement in our educational system is through privatisation … Vouchers are not an end in themselves; they are a means to make a transition from a government to a market system." Now in the UK we have vouchers, in the form of the pupil premium, that follow poorer children to whichever school they attend. We have academies that are "managed by trusts, companies limited by guarantee", as my old comprehensive school in Oxford is now tagged. We are currently travelling on Friedman's road map. Geographical comparisons show that it is not a good route to take.

Stefan Collini, professor of English literature and intellectual history at the University of Cambridge, when commenting on the latest international education statistics last year, explained that "countries committed to high-quality comprehensives, such as Finland, yet again come out on top. A stratified and class-segregated school system is not the answer: it's the problem." There is way too much hierarchy and stratification among UK schools. Across the European mainland, children are far more used to almost all going to local state schools. That may be because almost every other European country is more economically equal than the UK.

The UK's education system is beginning to look more like that of the US than other countries in Europe. Many American private universities now spend just a sixth of their fee income on teaching. These private providers take more than a fifth of fees in profit and spend even more on marketing to cover up the poor quality of what they are offering – subprime degrees not worth the paper they are printed on being sold to very young, very gullible consumers.

Since 2010-11 in Britain the new fully private universities have had access to taxpayers' monies and can make a profit. Pundits now talk of "the subprime student loan" because often what is being bought through borrowing is not worth the initial fee, let alone the interest on that fee. Yet not all privatisation in education is on an upward trend.

For four of the last five years the numbers of children enrolled in fee-paying schools in the UK have fallen to just over 500,000. Part of the reason for the fall is that the average annual private school fee is now £14,000, and one of the reasons it is so high is because the numbers are dropping. Average annual fees for boarding schools are £27,612 – but almost £29,000 for boarding sixth-formers. The number of pupils in those schools dropped by 1.4% recently, to 66,605. At the most elite boarding schools, once the price of school trips is factored in, costs can be £50,000 a year, per child.

At exactly the same time that fewer children at or near the top of British society are able to aspire to what the children of the top 1% can afford, millions of children at the bottom of the 99% are falling into poverty or seeing their poverty deepen. In 2013 the Children's Commissioner explained what is happening in the UK due to the nature of cuts and austerity: "Families with children will lose more of their income than families without children. However, lone parents will lose the most out of everyone." Within the 99% there is still rising inequality for the children.

Social mobility is lowest where local "choice" in education superficially appears to be highest. Another study last year named Trafford in Greater Manchester as having the highest level of educational social segregation. This is due to secondary moderns and grammar schools being retained there as well as private school provision being high. When confronted with the evidence that government education policy was reducing social mobility in such areas, a spokesman for the education department said it did not wish to comment on the report.

For schooling, the country to which utopians look is Finland, where 99.2% of school education is state-funded. In Finland, there is no inspection of teachers, no league tables; pupils are not set or streamed, and, as Diane Reay, professor of education at Cambridge, explains: "In four international surveys, all since 2000, Finnish comprehensive school students have scored above students in all the other participating countries in science and problem-solving skills, and came either first or second in reading and mathematics. These results were achieved despite the amount of homework assigned in Finnish schools being relatively low, and an absence of private tuition."

We have an educational system that is designed to polarise people, one that creates an elite who can easily come to have little respect for the majority of the population, who think that they should earn extraordinarily more than everyone else, and defines the jobs of others as so low-skilled that it apparently justifies many living in relative poverty.

The elite is shrinking. It really is now only 1% of the population who are maintaining their very high standard of living. The majority of graduates, even from a university like Oxford, cannot expect to fit within that 1% even if they all wished to only do the kinds of jobs that pay so much. The majority of all our young people should expect to see their standard of living fall in future, or they need to learn how to better control the richest people in our society. The 1% are disproportionately made up not of people who are most able, but of those who are most greedy and least concerned about the rights, feelings and welfare of other people.

Recently released findings from psychology suggest that many of them may be naturally inclined to be more selfish. It is not so much their fault that they find it hard to understand others' feelings. It is our fault for not controlling the greed of a few and for so long swallowing their shallow arguments as to why they deserve so much.

• Danny Dorling is Halford Mackinder professor of human geography at Oxford University. This article is an extract from his inaugural lecture, given this week.