On his penultimate day as First Minister last year, Alex Salmond unveiled a huge commemorative stone at Heriot-Watt University inscribed with the words he uttered in March 2011: “The rocks will melt with the sun before I allow tuition fees to be imposed on Scotland’s students.”

It was classic Salmond, using emotionally charged rhetoric in an attempt to render any dissenting voices illegitimate. It was also a microcosm of how the SNP has attempted to shut down any criticism of its higher education policies, and the choice that it has made to prioritise no tuition fees, something that disproportionately benefits the middle-class.

The SNP’s rhetoric cannot disguise an underlying truth. If you are a disadvantaged young person today, your chances of going to university are far worse if you are born in Scotland than south of the River Tweed. The poorest fifth of Scots are 3.5 times less likely to go to university through Ucas than the top fifth; the difference is only 2.5 times in England. Based on this measure, Scotland has by far the greatest level of educational inequality in the UK. (About one-third of Scottish students go to further education colleges, rather than to universities on Ucas).

“Ability to learn, rather than ability to pay,” defined the Scottish higher education system, argued the Scottish Government’s Independence White Paper. It is a seductive notion, but has long since been exposed as a myth.

Over the past 15 years, the Scottish government – not just the SNP, but Labour and the Liberal Democrats north of the border and for a period even the Scottish Conservatives too – has been faced with a political choice. It could prevent students from having to pay any tuition fees, or it could invest the money in more generous grants to help poorer students with their living costs. By plumping for free tuition, it has chosen the option that is most beneficial to advantaged students, and least helpful for disadvantaged ones.

It is populism for the middle-classes. Maintaining free university tuition while cutting grants to students from lower-earnings families equates to a £20 million transfer to middle-class students at the expense of less advantaged ones, Lucy Hunter Blackburn, a policy analyst, has calculated.

The poorer you are in Scotland, the more debt you leave university with. Last year, students eligible for the maximum bursary had average annual borrowing of £6,650 a year, £2,000 more than those ineligible for a bursary. This means that poor Scots leave university with an average debt of £26,600 (Scottish degrees are four years). Disadvantaged Scottish students also receive ess financial support while at university than their English counterparts: in 2015/16 Scottish students from households earnings £17,000 to £23,000 living away from home receive £559 a year less in financial support than those in England do, as research from Hunter Blackburn shows. These Scottish students have to borrow £5750 a year compared for their living costs, compared to £4,047 in England, where far more of the money comes in the form of grants rather than loans. Giving poor students both punier living support and saddling them with greater debts is a funny sort of progressivism. (By replacing maintenance grants with loans, England is now moving towards the model of leaving disadvantaged students to graduate with the most debt, although they will be able to access more generous financial support while studying.)

Because of the absence of tuition fees, universities themselves also lack money to invest in bursary and outreach programmes, further handicapping disadvantaged students. English institutions spend over three times as much on financial help for poor students, according to a 2013 study from the University of Edinburgh. English universities also no longer have a cap on the number of students they can take; the cap on the number of Scottish students that Scottish universities can take hurts all students but disproportionately affects the most disadvantaged.

In an age of austerity, cutting school funding has partly paid for protecting free university education. Spending on schools in Scotland fell by five per cent in real terms from 2010 to 2013 while, in England, it rose in real terms between 2010 and 2015.

Disadvantaged students in England have also benefited from how universities have been forced into being more proactive by the Office for Fair Access, an independent public body formed in 2004. OFFA has a ‘nuclear option’: the power to prevent universities charging full tuition fees if they are not doing enough to encourage disadvantaged students. Scotland lacks an equivalent single-focus regulator. “It doesn't work for them as well,” says Les Ebdon, Director of OFFA. “Scottish university funding agreements are not as effective as an independent regulator.”

After a decade of inertia improving university access, at least Scotland has belatedly accepted that it has a problem. The Commission on Widening Access in Scotland came into being this year. One of the problems its interim report identified was an “Inconsistent approach to using data to identify those who are socioeconomically disadvantaged.” So the Scottish government has been bad at producing data allowing its record on disadvantaged students to be judged, making comparisons with the rest of the UK very difficult.

Nicola Sturgeon is fond of saying that university debt would have meant she couldn't go to university. This is not only disingenuous – students only have to repay their fees when they are earning over £21,000 – but also ignores that students in Scotland today still leave university with an average debt of £21,000, more than those in Northern Ireland or Wales, which both have tuition fees. When far less generous bursaries from universities are taken into account, many disadvantaged Scottish students will actually graduate with higher debt than equivalent students in England. Perhaps this is why even Scots are becoming sceptical about this middle-class hand-out by stealth: only a quarter of Scots believe that no students should contribute towards their tuition fees.

The SNP will not be "letting the rocks melt with the sun" anytime soon. But if they did, it would help disadvantaged students north of Berwick-upon-Tweed get a better deal.