Ever topical and with an eye on the headlines, Justin Welby has joined calls – including from Jeremy Corbyn, the Labour leader – for tuition fees to be scrapped.

He was echoing a passage in his new book, Reimagining Britain, in which the archbishop of Canterbury lamented 'the disastrous move of privatising university education through increasingly high tuition fees,' adding: 'The 2017 Labour election manifesto motivated students in its recognistion of the need for a return to no-fee based funding of universities, although the cost implications of such a step are clearly considerable.' 

Now, interviewed by students at Canterbury Christ Church university, Welby said that fees should be paid for by taxation. He said: 'People like me who didn't pay tuition fees ... came away from university feeling like the country had given them something and they owed it. If you've paid for it, you've bought it, it's yours – why should you care about anyone else?'

That is a powerful point, and Welby is surely right about the dangers of an increasingly individualised and, frankly, selfish culture.

But is he – or for that matter Corbyn, Ed Miliband, the Liberal Democrats, the SNP and the rest – right in thinking that it is progressive to oppose the concept of people paying for their own higher education, especially when using what is now, effectively, a graduate tax as opposed to the upfront payment of thousands of pounds that I, for one, had to make?

Arguably not. Because graduates still earn more than non-graduates, and there is nothing progressive about forcing the general tax payer, many of whom have not been to university, to subsidise what is still, despite massive expansion in recent years, a privilege for those who do.

Indeed, the idea of going to university for free at a cost to ordinary people is nothing short of a scam for the wealthy.

Instead, the policy of tuition fees and even that of top up fees, introduced under Tony Blair, expanded rather than narrowed access to higher education.

Not that the Tory government would ever argue in this way, of course, but the policy is an all-too-rare hit on middle-class parents for whom free higher education had long been a perk that soaked up funds that should have been spent on state schools. Perhaps this is why Charles Clarke, an education secretary under Blair who brought in £3,000 tuition fees, is said angrily to have told a student who questioned his left-wing credentials that if he were 'a real socialist' he 'wouldn't spend a penny on higher education'.

Then there is the cost. The price of scrapping tuition fees is estimated to be £11 billion, and wiping off student debt would reportedly cost £60bn. What would such a cost mean for public services? It is little known, meanwhile, that students currently pay on average roughly 65 per cent of the cost of a degree through fees, while the taxpayer anyway subsidised around 35 per cent, through teaching grants and loan subsidies.

Next, the evidence. The universities admissions service, Ucas, states that in 2015 application rates for 18-year-olds living in disadvantaged areas in all countries of the UK actually 'increased to the highest levels recorded'. At the same time, the university inequality gap is falling. In 2006, advantaged UK 18-year-olds were 3.7 times more likely to apply than disadvantaged 18-year-olds; and by 2014, when the higher fees had come into force, that ratio had fallen to 2.4.

In Scotland, where there are no fees under the nationalists, the wealthier parents and pupils are of course benefiting. A study into student funding across the UK for the Centre for Research in Education Inclusion, and the Economic and Social Research Council in 2014 found that while free university tuition coupled with cuts in grants to lower-earning students means middle-class families in Scotland are £20m a year better off, the overall costs to poorer students have gone up by at least £32m per year.

As the archbishop of Canterbury in a Church of England that remains (for better or worse) established, Justin Welby is more than entitled to speak out on hot political issues of the day, as I gather his correspondence secretary likes to points out to those who write in objecting to certain political statements. And as my colleague Harry Farley has noted, he is a highly political archbishop.

But that does not mean he is always right, and on tuition fees – unlike on so many other crucial areas – he is certainly not being progressive.