Britain’s higher education system is in such dire need of reform that it’s hard to decide which problem should be tackled first. In his latest outing as a Telegraph columnist last Thursday, Nick Timothy, former chief of staff to Theresa may, wrote that students should be given more of an incentive to shop around for the best education deals. In classic Timothy style, he argued that this incentive could be manufactured by the state. The Government should force under-performing universities to close, and should replace them with government-run colleges providing short courses designed to equip participants with “marketable skills”. The fees for these colleges would be capped to make them more appealing to students. This model, he believes, would give students more choice and inject some much-needed competition into the university market.

The architect of the Tory manifesto at the last election may be right that there are too many universities providing worthless degrees, but considering that he lost both his job and the Conservative commons majority arguing for more state intervention in the private sector (remember the energy debacle?), it’s alarming that he still thinks that Government caps are the way to solve the problem. To anyone who has been watching the university saga come to the boil – fat-cat vice chancellors one week, compounded interest rates punishing success the next – it is crystal clear that what universities need is less state intervention, not more.

British universities of all calibres (with the exception, perhaps, of Oxford and Cambridge) have a serious problem with student accountability. In the years since my graduation, I have heard from my alma mater twice. Once, six weeks after leaving, I received a call at 8 on Sunday evening from an apologetic undergraduate asking if I would be willing to donate to my old university. For one term in second year I worked part-time in the same fundraising team (the worst ten weeks of my life) and so sympathy stopped me biting her head off. Donate to my university? I was £45,000 in debt thanks to my university education, and, if I ever managed to secure a job, would cough up 9% of my earnings above £21,000 to Student Finance every month for rest of my life. I could think of better ways to spend the other 91%.

The second time, one year after graduating, I received a call from someone in the careers department who was compiling a list of graduate destinations for the new prospectus and wanted to know what I was doing now. I explained that I had just left a job I was hating in financial PR and was currently freelance writing in the hope of finding an opportunity in journalism. I was expecting some support or advice; he responded by asking me if he could just put down “analyst in the financial PR sector” because the formatting looked untidy if my job title went on to two lines.

Universities get away with this because the public are too confused to call them out on it. As higher education institutions feature such a diverse range of interested parties (government, private research, endowments and fees all contribute towards the funding) no one can quite decide whether they are predominantly public bodies, or predominantly private companies with charitable duties.

The eye-watering salaries paid to vice chancellors would indicate that universities are beholden to market forces – VCs are paid along the same lines as CEOs of successful, medium to large businesses – but the laissez faire attitude towards students is something that would normally only be tolerated in the squeezed public sector.

A comparison with the school system throws the problem into sharp relief. At prestigious British public schools, school fees include not only a high-quality education, but also career support and social networks, “old boys’ clubs”, which last a lifetime. These schools have charitable status but they operate as businesses. Staff are directly accountable to their customers – their pupils’ parents – and staff pay correlates with demand and supply. Schools which are satisfying their pupils’ parents thrive, schools which aren’t do not last. In contrast, in the state sector, education is provided for free by the Government, pay is capped to keep costs down, teachers are not directly accountable to parents, and when something goes wrong, the state shoulders at least part of the blame.

Universities have a similar funding structure to private schools: student fees and endowments now make up over two thirds of university income, and vice chancellor pay is calculated to “reflect the market”. Yet with few teaching hours and a severing of ties after graduation, the customers – the students – aren’t getting any of the perks regarded as part of the package at private schools.

In a nutshell, students are getting the worst of both worlds.

What’s more, because the public vaguely grasps that the state is in some way tangled up in the higher education sector, it is the government, not universities, that gets blamed for failings and asked to compensate students accordingly.

A common argument among graduates is that they feel burdened by their student debt. Fair enough, I’m with you there. But then the logic goes a little awry. Student debt is a burden therefore Corbyn is right to argue that the Government should pay it off using public money.

What? If something is not providing value for money – and therefore becoming a burden – surely it should be redesigned so that it does provide value for money, not funded in its sub-standard state by tax-payers? If a TV manufacturer was routinely producing faulty TVs and the Government stepped in to fund it, I imagine consumers would have something to say about it.

In October 2014, a paper by the entrepreneur Peter Ainsworth for the Institute of Economic Affairs proposed a radical new model for student funding which would combat this problem by establishing a direct link between universities and their graduates. He suggested that rather than the Government fronting the cost of higher education and footing the bill when graduates default on their debt (the current system), universities should individually offer contracts to their students, who would agree to pay to the university they attended a given percentage of their earnings after graduation. That percentage could vary by course and institution.

Essentially, the university would be taking an equity interest in the graduate premium earned by the student.

Under Ainsworth’s model, universities would have a much stronger interest in the employability of their graduates, and that interest would continue after graduation. What’s more, given that universities would have entirely independent funding streams, they could be released from all regulation of undergraduate courses. They would become free to innovate, develop cheaper part-time courses using online provision, and so on.

There would, at last, be proper competition between universities. But, unlike in Timothy’s plan, competition would lead to a”‘race to the top” and not a “race to the bottom” because universities would have a direct economic interest in the success of their students after graduation. Universities which refused to give their students a value for money education would reform out of market necessity.

Ainsworth’s overlooked paper from three years ago doesn’t have all the answers – but if the central proposal was adopted it would definitely be a step in the right direction. In the free market, all companies are directly accountable to their customers: if a company provides value for money it thrives, if it does not, it will pretty quickly lose custom and will eventually go bust.

If our broken higher education system is to be fixed, it needs to start playing by market rules.