The Labour Party manifesto promises a National Education Service on the model of the National Health Service. Angela Rayner, the shadow education secretary, announced some of the policies ahead of the manifesto launch: six years of free post-16 education for every adult across their lifetime, paid time off work for education and training, and maintenance support for those on low incomes.

A teenage mother who left school without qualifications, Rayner trained as a care worker and made her way to national politics through the trade union movement. It’s extremely unusual for a person of her background to climb to the heights that she has. And it’s incredibly difficult for a person of her background to find a way back into the education system after leaving it, for whatever reason. Rayner was no doubt hard-working, gifted and determined, but – as I’m sure she’d acknowledge – she was lucky, too.

I started my degree when I was 23. Before that I was working to support myself and, when I could, my mother and two younger brothers. My mother had been made redundant when I was 15 and was unable to find meaningful or steady work. Money was extremely tight, home was unstable, and both my brothers left school at 15, without any qualifications. When I moved to London, aged 19, I was lucky, twice. First, because I found a job with a small company where the owner recognised my potential. And second, because of Birkbeck College, which allowed me to take a degree by studying in the evenings.

When my mother died, a few months before I started at Birkbeck, my teenage brothers came to live with me. They did not have my luck. Their break with education had been too great, their home life too chaotic for too long, and I couldn’t support them financially. One took his life. The other eventually took a one-year hairdressing course. It was a profession to which he was singularly unsuited but, in our panic to find something, it was the only course available. It wasn’t a success, but that was his one chance. So, he has struggled the last fifteen years, with apparently endless cheer and wit, simply to survive.

On hearing Rayner’s proposals, I thought about how different it could have been, the suffering that could have been spared, if my mother had been able to retrain for free, if both my brothers had been able to access maintenance funds to support them back into education or training, if there had been a second chance for each of them. None had my luck, but why should they have needed it?

The possibility of education, in the widest sense, is the greatest defence against the power of bad luck. And yet, as an incredibly rich society, we have put access to education into luck’s hands, too. Unless you are in possession of material wealth – the particular form of luck that we seem to value most – you won’t succeed unless nothing goes wrong between the age of four and early adulthood, and nothing much had better go wrong afterwards, either. Those are odds that even the most reckless gambler would hesitate to accept.

For the past eight years, I have taught philosophy at Oxford, a place that floats on a murky sea of good luck, mostly of the financial kind. It slicks a candidate’s path to the admissions interview (nearly 40 per cent of undergraduates at Oxford went to private schools, and most of those who were state-educated are comfortably middle-class). And even for those who make it as far as the interview, luck still plays a role in deciding which of the clever, hard-working applicants get places.

But that isn’t the story they’re told: they’re told it’s a question purely of merit, or even fate, like the Hogwarts sorting hat. And in part because of the pipeline from Oxford – and places like it, though there aren’t many places like it – to positions of power, that false and lazy story finds itself replicated in the establishment: everyone is where they deserve to be. To build a National Education Service is to reject this fantastical notion. By facing up to the power of luck, we may glimpse a world in which it’s no longer needed to get by.