Scandals aren’t meant to happen in British universities. Parliament, tabloid newsrooms, the City … those we expect to spew out sleaze. Not the gown-wearing, exam-sitting, quiet-in-the-library surrounds of higher education.

Yet we should all be scandalised by what is happening in academia. It is a tale of vast greed and of vandalism – and it is being committed right at the top, by the very people who are meant to be custodians of these institutions. If it continues, it will wreck one of the few world-beating industries Britain has left.

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Big claims, I know, but easily supportable. Let me start with greed. You may have heard of Professor Dame Glynis Breakwell. As vice-chancellor of Bath University, her salary went up this year by £17,500 – which is to say, she got more in just one pay rise than some of her staff earn in a year. Her annual salary and benefits now total over £468,000, not including an interest-free car loan of £31,000. Then there’s the £20,000 in expenses she claimed last year, with almost £5,000 for the gas bill – and £2 for biscuits. I knew there had to be a reason they call them rich tea.

Breakwell is now the lightning rod for Westminster’s fury over vice-chancellor pay. As the best paid in Britain, she’s the vice-chancellor that Tony Blair’s former education minister, Andrew Adonis, tweets angrily about. She’s the focus of a regulator’s report that slams both her and the university. She’s already had to apologise to staff and students for a lack of transparency in the university’s pay processes – and may even be forced out this week.

But she’s not the only one. The sector is peppered with other vice-chancellors on the make. At Bangor University, John Hughes gets £245,000 a year – and lives in a grace-and-favour country house that cost his university almost £750,000, including £700-worth of Laura Ashley cushions. Two years ago, the University of Bolton gave its head, George Holmes, a £960,000 loan to buy a mansion close by. The owner of both a yacht and a Bentley, Holmes enjoys asking such questions as: “Do you want to be successful or a failure?” Yet as the Times Higher Education observed recently, he counts as a failure, having overseen a drop last year in student numbers, even while being awarded an 11.5% pay rise.

Compare these fortunes to that of rank-and-file university teachers, who have seen only a 1% rise in their basic pay in the last year. Or consider that on the sector’s own statistics, most academics are on some form of casual contract, including being paid by the hour for marking and teaching. It is not uncommon in English and Welsh universities for students to pay £9,000 a year to be taught by an academic who isn’t earning that much. Reporting last year, I met one lecturer at a Russell Group university who had until recently worked a total of five jobs a week, including as a binman.

Bring up such examples and the universities will spin you a version of what Rick Trainor, former principal of King’s College London, once said: “If you want the best, you have to pay the best.” What they won’t mention is the finding of the University and College Union that more than seven out of 10 vice-chancellors are either members of the committees that set their pay, or can sit on them – as Bath’s Breakwell did.

Seven out of 10 vice-chancellors are either members of the committees that set their pay, or can sit on them

If this were just about individual greed, we could sling out a few bad apples and carry on. But what’s rotten in universities is the rules observed by the people at the top. And what’s at risk is the reputation of our entire higher education system.

Let us revisit Bath. Like nearly all British universities, it is a charity that is committed to serving the public good, as recognised by the public with tax exemptions. As with most charities, the buck stops not with its vice-chancellor but with the trustees – or, as they are termed at Bath, the council. These are the people the public rely on to challenge management and uphold the institution’s values. Bath has 26 councillors, including the vice-chancellor and a smattering of representatives from faculties and students.

By far the biggest number – 14 – come from outside the university, and what’s striking about them is how many are from finance or business: the CVs burst with names including Rothschild Asset Management. Councillors from the auditing giant PwC alone outnumber student representatives. The committee that sets Breakwell’s pay is chaired by a commercial lawyer, with two other positions held by someone from PwC, along with the head of a construction company.

These aren’t people who will argue with a vice-chancellor getting half a million pounds. They won’t bat an eye over jacking up rents for students, even though Bath is already making millions out of its accommodation. I wouldn’t expect such a narrow club to raise questions over the university’s use of zero-hours contracts. Nor are they representative of Bath, where there is a serious housing shortage and growing resentment over local inequalities. Directors of an accountancy? Sure. But not guarding the values of a charitable enterprise and a place of intellectual enquiry.

Ten years ago, British finance was held up to the rest of the world as a joke – full of flyboys paying themselves truckloads of money and running some fine old institutions into the ground. The result was a crash, a bailout and an economic slump that still drags on.

Yet the people running our universities are now busy importing that failed model, along with all its business bullshit. If they succeed, they will trash our higher education system. At Manchester University, half the outside trustees come from business and finance. There is no major non-profit figure, nor a housing association representative (which would make sense, given the university provides a lot of student housing).

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There is, however, a lot of AstraZeneca, where the university’s vice-chancellor Nancy Rothwell has served as a non-executive director: two members of her leadership team come from the pharmaceutical firm, while three trustees are either current or former employees. The university justifies this as just deserts for “a big, local employer”. What they couldn’t tell me was why they didn’t offer such representation to the Bishop of Manchester (as the university used to do) or to a major trade unionist. When the university managers launched a plan to make 140 academics redundant, they didn’t even bother to consult the senior academic body of the senate. Rothwell also sat on her university’s pay committee, according to the UCU, as did Hughes and Holmes.

They talk about making the university world-class while threatening its world-class school of languages with swingeing cuts. The result has been extraordinary: just as happened at Bath, staff at the school of languages have passed a vote of no confidence in their university’s management. Some have left; others have simply lost the goodwill that traditionally underpins academia.

Our universities, the NHS and the BBC: three things that the rest of the world admires about Britain. It is no coincidence that all of them derive their values and ethics from outside the marketplace. If we want to ruin them, the quickest way is to bring in the values of finance and business – of profiteering from students, sweating academics and handing riches to the management.

• Aditya Chakrabortty is a Guardian columnist