One by one, the great institutions that bind Britain together are being allowed to fray, weaken and decline. They may do good and even vital work, but whatever their purpose – from the system of legal aid to the Open University – they are under siege. Britain might be substantially richer than it was 40 or 50 years ago but the national narrative is that organisations once energetic and growing are now unaffordable. The overriding moral imperative is to lower allegedly insupportable taxation, not to create public goods or sustain the institutions that bind.

Last week, it was the Open University that was in the news as its beleaguered vice-chancellor resigned after a mere three years in the role. He may have been right about the necessity to re-engineer the institution, to refocus it on lifelong learning and find savings, given the 20% fall in its income. But the scale of the proposed redundancies – more than a quarter of the workforce – felt to the academics and the wider staff swingeing. There was too little valuation of research, a crucial component of any university. There may have to be change, but not to put the very idea of the OU at risk.

Ten days ago, they voted against him in a resounding vote of no confidence.

Some of Peter Horrocks’s initiatives deserve a better hearing than they received, notably the proposal to make the OU the world’s leading online university. But managing necessary change in any institution against a backdrop of despair at a darkening future is close to impossible. As a leader, you have to offer hope and Horrocks, for reasons largely beyond his control, could offer too little of that. Brexit Britain is no place for hope. His resignation is a small tragedy for him but a bigger one for the country.

The OU, for all its achievements as one of Europe’s leading higher educational institutions, with more 170,00 students, is a Cinderella of our higher educational system. One of the more inspiring afternoons in my life was witnessing and speaking at an OU graduation ceremony. Up to the stage came mature men and women who had studied, against the odds, to win themselves the degree that circumstances had denied them when they were young.

The uninhibited cheers, the Mexican waves and the tears were not the stuff of your common or garden graduation. One woman, partially disabled, had worked 15 years for her degree; another was so intensely moved that she needed assistance to collect her degree. You don’t often find so much good and heart on offer anywhere – and I inwardly congratulated the greatly undervalued Harold Wilson, who had the vision to found the institution despite widespread scepticism.

The former chancellor George Osborne, bequeathed an unsustainable public deficit by the deepest and longest recession for a hundred years induced by the near collapse of the western financial system, had choices about how to react. He could have combined spending cuts with tax increases; instead, he organised what will be seen in years to come as one of the great acts of social vandalism by diminishing a series of great public and social institutions.

To name but a few: there are a third fewer Sure Start centres; the national dental system is a joke, with sales of DIY dental kits booming; the criminal justice system is reeling; local authorities can offer little more than their statutory obligation to provide social care; our armed forces are denied key equipment. And while the impact of making the entire post-18 education system dependent on students incurring debts approaching £50,000 has been surprisingly slight on undergraduate-admitting universities, it has devastated those, such as the OU, which serve older, part-time and mature students.

For older students, there just isn’t the time in their remaining career to pay back such debts and they also have the commitments of family. The 1970s were economically tough, but governments of both political hues threw their protective mantle around mature and part-time students – the OU’s student numbers boomed to more than a quarter of a million. Since 2012, when fees rose to £9,000, applications have plummeted by around a third. The OU has been left with a cost structure out of kilter with its now depleted revenue.

Jeremy Corbyn at least put student debt decisively on the political agenda and there is now a committee under the leadership of Philip Augar, charged by Theresa May with assessing reform options, with phasing out the whole system expressly excluded. But there is still scope for more limited reform for mature and part-time students. Put bluntly, unless the state assumes more share of mature students’ fees, Britain can say goodbye to offering older adults a second chance or any system of lifelong learning.

I doubt the Department for Education will listen. Although the 1944 Education Act enshrined the principle that “the nature of a child’s education should be based on [their] capacity and promise and not by the circumstances of [the] parent”, successive Tory secretaries of state have found the commitment irksome. And, if anything, the attitude towards mature students is the thin end of the wedge. I learn that, post-Brexit, DfE officials are considering making all non-UK nationals pay for their children’s education, introducing an apartheid system into our national education. All Brexit supporters should hang their heads in shame.

The Eurosceptic right is biding its time until Britain has left the EU next March and then it plans to join battle in earnest. Great social democratic institutions such as the OU can take their chance in a marketised university system and if they can’t swim they will sink. Horrocks, however clumsily, was trying to make the OU swim. The pressures are going to become more, not less, intense.

• Will Hutton is an Observer columnist