Last week, the Sutton Trust called on elite UK universities to make a ¡°radical change¡± to their admissions policies by significantly increasing the number of reduced-grade offers they make to disadvantaged students. The call was made in the wake of criticism of the universities of Oxford and Cambridge for admitting so few black students ¨C which, former education minister David Lammy, amounts to ¡°social apartheid¡±.

Such storms regularly recur because inclusivity matters a lot. Few people would deny that a university should be a haven for all talents, regardless of background: an elite university even more so. But there are limits, and these limits are, above all, political. How far are politicians and vice-chancellors willing to go to guarantee equal access to elite universities that have become only more attractive as ever greater proportions of the population access higher education?

Of course, there has been real and welcome progress over the past few years in promoting access to elite universities, and this is not to be disparaged. For example, children from disadvantaged areas of the UK are 52 per cent more likely to go to highly selective universities than they were in 2009. Even from a low base and against a background of increasing places, that is impressive. But it is not easy to see this rate of progress being maintained without more drastic action being taken to shift the stubborn inequities that characterise the fortunes of certain socio-economic and ethnic groups, such as quotas, lotteries or crafting classes to reflect all kinds of different talents and backgrounds.

Elite universities and government still rarely advocate such actions, however, because they would conflict directly with the fact that elite universities are precisely the ones that produce elites ¨C whose existing members would stand to lose the most. That¡¯s why top universities tend to emphasise both their elitism and their inclusivity. They shout loudly about the latter, while knowing full well that they are also part of a chain of educational inequality.

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In the US, the position is starker. The old leisured elite, previously focused on conspicuous consumption, has increasingly become what University of Southern California social researcher Elizabeth Currid-Halkett calls an aspirational class. Its members compete in a fierce form of meritocracy that necessitates ever greater spending on ¡°inconspicuous consumption¡±, such as investments in their children¡¯s education. The top 10 per cent of US households now spend almost four times as much on this as they did in 1996.

From their earliest days, the children of such households have to run on a treadmill to gain access to the best schools and then universities. This requires engaging private tutors, seeking out all kinds of juicy extramural activities, demonstrating powers of leadership and gaining only the best placements. Social media makes things worse by providing a platform on which these children constantly compare themselves with others. No wonder many live in a permanent state of anxiety, which is manifested in, for example, their increased use of antidepressants, counselling and therapy.

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In the UK, too, a middle-class educational arms race has developed ¨C although at generally lower levels of expenditure ¨C as, understandably, parents try to do the best for their children. Even ignoring the issue of private schools, there are still plenty of other investments to be made. Moving house to access the best state schools has become commonplace. Private tutoring is becoming a must-have. Children are obliged to participate in all kinds of extramural activities so that their CVs stand out, usually at an extra cost. The opportunities opened up by unpaid internships are also hoarded by the middle class. And the tempo of this meritocratic competition is increasing. By the time these children get to university, investment in them will already have been very substantial, and will likely continue with a postgraduate leg-up.

Importantly, all this is taking place against the withdrawal of many middle-class privileges, such as pension tax relief and a general squeeze on some middle-class incomes that is starting to fuel genuine anger (just look at one of the chief demands of middle-class populism: the abolition of tuition fees). Increasingly, even the better-off segments of the middle classes often see themselves as victims.

It isn¡¯t just about austerity. It¡¯s also a more general sense of grievance, part of which comes from the feeling that their children are having to work ever harder just to stand still ¨C even when the meritocracy has been carefully structured to make sure that they are the winners. Even after all that educational investment, the life chances of their offspring may be restricted in comparison with theirs: something that grates on both children and parents. Under these circumstances, restricting access to elite universities in order to admit others would be just about the final straw for the middle class, and a very brave political move.

The result is that politicians and vice-chancellors of elite universities will continue to promote inclusivity, but only up to a point.

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Sir Nigel Thrift is the former vice-chancellor and president of the University of Warwick. He has just stepped down as the executive director of Schwarzman Scholars.