I wore a miniskirt and fishnets to my registration at the University of Cambridge. Not for any particular reason: they were just items of clothing I had to hand. I woke up, got dressed, slipped on my tattered cherry-red Doc Martens and headed to the Old Library. There, I was greeted by a row of students all dressed in suits and ties, or demure black or navy dresses, and gowns.

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I had no idea that registration at Cambridge, and the four-course meal that follows it, is a formal dress affair. That was my introduction to Cambridge life: sitting in an oak-panelled hall, wearing a borrowed gown, swarmed by cutlery and glasses (they have one that is just for port), listening to the misadventures of someone who’d spent her gap year volunteering at an art gallery in New York.

As one of the 6% of care leavers who attend university, and one of the just 2% of Oxbridge pupils who come from a free school meals background (13% of secondary pupils receive free school meals), I could tell you a dozen more anecdotes like this. So last month’s verdict from Les Ebdon, director of the Office for Fair Access, that Oxford and Cambridge need to do more to improve access for students from disadvantaged backgrounds, came as no surprise to me. Of course there are access issues at Oxbridge. But for progress to be made we need to understand this issue as cultural and psychological, not just economic – albeit a culture that’s intrinsically linked to one’s economic background.

The most pernicious assumption that’s made about those of us who are marginalised is that certain things are simply “not for the likes of us”. This often isn’t a subtle message, either. A good number of people I encountered when I was still in care told me this was the case: from the admissions staff at the prestigious grammar school who categorically said to me that they don’t take students from “unsettled circumstances”, to the Oxbridge access adviser who informed me that most applicants had seven A*s at GCSE, and that with my own paltry five, I shouldn’t put myself through the pain of applying.

But it’s not just those above you who lower your expectations and make you doubt your aptitude. Indeed, I’ve often found that it’s my peers who have proved the fiercest doubters. Yet these doubts often stem from a lack of understanding. To illustrate: a friend of mine, who’s also spent time in foster care, and who’d never considered university for himself, was amazed to hear about loans and grants. He’d just assumed the costs came out of your own pocket. Lest you think he was stupid, you’d do well to consider how much you know about life choices you’ve never contemplated. I certainly didn’t know about the full extent of financial support available at Cambridge until after I’d arrived.

These issues are only compounded by the experience of growing up in the care system. Children in care have often been the victims of neglect, sexual, physical and emotional abuse, bereavement or other traumas. The experience of repeatedly being told – or made to feel – by those responsible for your care that you are worthless, stupid or unwanted is almost impossible to describe if you haven’t been through it first hand.

Many solutions have been proposed, such as lowering entry grades for students from marginalised backgrounds, which I support. But such remedies will only ever help the tiniest fraction of those targeted, as so few care leavers even get to the point where a lower grade requirement may allow them to apply.

Instead, what is needed is a radical overhaul of the way we conceive of social mobility in this country: from the merely economic, to the cultural. On Oxbridge’s part, this would entail a far more extensive outreach programme, making sure marginalised students are aware, from a young age, that Oxbridge is for them, and that money needn’t be an issue when they apply. Just meeting another student from a similar background can be an amazing encouragement (and not doing so can be a discouragement). And the government needs to ensure that everyone – no matter their postcode or budget – has access to culture, literature, art, politics and science: not just at school, but in their neighbourhood and community. Studying these subjects needs to feel possible for children and young people from all backgrounds.

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There’s a reason why I’ve succeeded where others like me have stumbled: a reason that’s not related to my hard work, tenacity, or intellect. I was born to two middle-class, university-educated parents. How I entered the care system is a story for another time, but for most of my childhood I was surrounded by books, art and culture. It was not a lofty dream for me to apply to university; four of my five older siblings had already done so, and almost every member of my extended family expected me to do the same.

In my experience, nobody gets anywhere worth going without some degree of privilege. Our most important job is not to celebrate those who might have “pulled themselves up by their bootstraps”, but to ensure that those born with little social privilege have access to the information and cultural advantages that most people reading this can probably take for granted.