David Cameron publishes his memoirs today, in which he looks back on his time at Eton college; and back on the drug use that, had he been from a different background, might have landed him in jail. Eton is proud of its political leaders. This can be seen from the fact that, in one of its most famous rooms, you can find the bust of every student who has gone on to become prime minister. Eton must ask itself, though, whether it is proud of the kind of leader that it is producing. It must also ponder why, if it truly sees itself as a school of leadership, there are more and more people who regard it and similar institutions as utterly unfit for purpose.

A few weeks ago, like thousands of other people, I shared a photo of Jacob Rees-Mogg on social media. The photo, an image of him reclining in the House of Commons as he listened to his furious opponent in a debate about Brexit, seemed to be the very image of entitlement. At a time when the country’s economy and social fabric were under unusual strain, there was Rees-Mogg, apparently revelling in the bedlam.

It is unacceptable that, on the brink of Brexit, a country that claims to be global is directed by an ever more socially homogenous group

It is too easy for me and others who attended Eton to throw our hands up and say “this is not who we are”; to point towards all those kind, decent fellow alumni whom we know personally, maybe even at ourselves, and say that we are better than that. It is far too easy for us to say, in the style of men anguished by the revelations of the #MeToo movement, “not all Etonians”. Moreover, that response stops us from asking the hardest questions. Why, in recent years, has our school consistently turned out prominent politicians with a devastating lack of empathy for the most vulnerable people in our country? How – why – did we enable an atmosphere in which their obsessive sense of destiny was able to thrive?

Let us look briefly at some of those politicians. Not only do we have Cameron and Boris Johnson, who seems to be motivated by nothing but a desire to live in the country’s most prestigious house. We have Rees-Mogg, gleefully retweeting speeches by the far right. We have Kwasi Kwarteng, who has dismissed the report of the UN expert on extreme poverty; a report that found that the Conservative party’s austerity policies had inflicted “great misery” on the British people. We have Rupert Harrison, the mind behind a bulk of those policies. Late last year, Harrison referred to the most likely outcome of Brexit as “an orderly process” – even though, to all observers, it has been the very definition of chaos. Even Rory Stewart, praised by many as a moderate hope within his party, has voted consistently for measures that enabled and accelerated social inequality in the UK.

Facebook Twitter Pinterest Boris Johnson and David Cameron on an Underground train. Photograph: Stefan Rousseau/PA

The presence of so many old Etonians with regressive ideologies in our politics is not proof of our school’s intellectual brilliance. It is instead a grim indication of an economic divide in the UK so severe that the kind of people with the wealth and networks that make them likely to attend schools such as ours will increasingly end up in these positions. Before Cameron, there had not been an old Etonian prime minister since Alec Douglas-Home in 1964. Now they have been two of the last three to occupy No 10.

If I look back at my time at Eton, I fondly remember many of my teachers and peers, and I recall a place that gave me a world-class education. But it was also a place where many of the most arrogant students were routinely awarded with positions of authority. I regularly heard working-class people referred to as “lebbage” – a play on the Latin word (I know, I know) for “the common people”. Though the school has many more black students now – when I was there, there were no more than three or four out of about 1,250 at any one time – Johnson’s brand of humour was far from being an outlier. Come on, we were only teenagers, you might say, eventually people grow up. Well, looking at our politics, it is clear that several of those people have not grown up; they have merely aged.

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I am sadly not confident that Eton – the school and its alumni – is capable of looking at these issues in sufficient depth. A few months ago, I saw the headmaster launch a campaign in partnership with a national newspaper. The campaign was looking for applicants for a scholarship fund to study at the school; a current Eton scholar was smiling out from the newspaper’s pages. The newspaper was the Sun, and this brilliant student was the son of refugees – just a few years previously one of the Sun’s columnists infamously referred to such people as “cockroaches” in the same week that hundreds were drowning in the Mediterranean. A more self-aware institution would have sought a media partner with a history of greater empathy for working-class black people than the Sun.

It is unacceptable that, on the brink of Brexit, a country that claims to be global is directed by an ever more socially homogenous group. Whether Eton likes it or not, it cannot look at its most visible alumni – in effect, its ambassadors – in the political sphere and conclude that these are people who value compassion anywhere near as much as they value power. The UK deserves better leaders, from more socially conscious backgrounds, and it deserves them now.

• Musa Okwonga is a poet, journalist and musician