The student tuition fees system is broken, Justine Greening, the recently departed education secretary, all but admitted this week – and indeed it is.

When in 2003-04 Labour acted to raise university tuition fees from the initial £1,000 to £3,000, the alternative of a graduate tax was supported by the then chancellor Gordon Brown. I was in cabinet at the time, but the idea was never formally put to us, and instead it became tangled up in the Blair-Brown rupture that so damaged Labour in office.

I now wish it had been agreed. As the independent UK 2020 thinktank has just demonstrated, with the former Labour education minister Lord Adonis’s endorsement, the English student finance system simply isn’t working. It’s also punitive to all but students with the richest parents who pay off the fees and any loans.

I once marched against tuition fees. Now I can see their worth | Sonia Sodha Read more

None of us in the cabinet at the time ever envisaged the Tories’ £9,000-plus fees with mountainous student debts averaging £60,000 standing in the way of loans for cars or homes, and adding to young people’s real sense of intergenerational unfairness.

Nor would we have tolerated extortionate interest charges of more than 6% against a base rate of 0.5%, and an effective marginal tax rate of more than 40% when graduates trigger repayment after crossing the salary threshold of £21,000 (now rising to £25,000).

Fourteen years ago in cabinet discussions I was persuaded that fees were a means of switching public spending from those with degrees who would have much higher earnings in adult life, to focus on early years’ education which is absolutely crucial to life opportunities. All governments face tough choices on priorities, and this was an example.

A graduate tax would also offer a more sustainable stream of revenue for the Treasury

But today nearly half of England’s students default on repaying any of their fees back, and three-quarters don’t pay back the full amount – a colossal failure in a system that cabinet ministers like me were persuaded would reduce the Treasury’s debt and borrowing.

In 2014 it was estimated that, around the midpoint of this century, when the debt is written off, £90bn of the student support funded by the Treasury would remain unpaid. Since then the Tories have unforgivably withdrawn grants for poorer students, ensuring the unpaid debt will be even higher.

My former cabinet colleague and universities minister John Denham has estimated that English taxpayers spend £6 on debt cancellation for every £1 on teaching students. Privatising university teaching and shifting the cost from taxpayers to students and their families is plainly dysfunctional.

Moreover, other more successful economies have abolished fees. Germany did so in every state from October 2014, following Denmark, Finland, Norway, Sweden and Austria. The Dutch and the Swiss have modest tuition fees way below England’s, which are the highest in the world for public universities.

In January 2017, New York state announced plans to make state universities tuition-free for children from families earning up to $100,000 (£70,000) annually, extending to children whose families earned up to $125,000 by 2019 – a million families or the great majority in the state.

Governor Andrew Cuomo said the reason was that, by 2024, over 400,000 more jobs will require a degree or higher qualification in the state, and the cost of a degree was rising beyond what most American families can afford. (Ironic since there’s been a flow of English students to the US because the fees there are lower!)

In 2016, working-age graduates in England earned on average £9,500 per year more than non-graduates, while postgraduates earned on average £15,500 more. Over an entire working life graduates earn nearly £400,000 more.

Although it is right that graduates contribute to a privileged education most of their fellow citizens don’t enjoy, why not replace fees with a small addition to income tax, paid by all graduates throughout their working lives?

The Million+ thinktank suggests a 30-year graduate tax rate rising across income bands, with nothing paid on earnings up to £10,000 per year; 2% up to £25,000; 2.75% to £42,000; and 3.5% above that.

It's not about whether we charge tuition fees – in Wales we've found a third way Read more

Collecting this extra small tax through the HMRC would be much simpler, much more efficient and less costly than the current wasteful bureaucracy. And the clincher surely is that these small rates are very much lower than the 9% now compulsorily deducted from graduate workers above the threshold.

Although some maintain that a graduate tax would mean a “free ride” for students from richer families, they tend to go into higher earning jobs where they will more than pay back the fees they incurred. A graduate tax is the fairest, most progressive way of dealing with the financing of university students because the more you earn, the more tax you will pay. It would also offer a more sustainable stream of revenue for the Treasury, and thus is more fiscally responsible. A win-win for students, their families – indeed, everyone.

• Peter Hain was Labour MP for Neath from 1991 to 2015. He has held the posts of secretary of state for Wales, for work and pensions, and for Northern Ireland