The debate over the number of young people who should attend university is both crucially important and potentially extremely damaging. Recent events suggest that it is the type of issue on which governments might topple.

More importantly, it is an issue that will damage the lives of untold numbers of young people if we get it wrong.

Yet there is an extraordinary inconsistency in the present debate. A succession of governments have declared how many young people should attend university - 30 per cent, 40 per cent and now even 50 per cent. Yet to my knowledge there is no hard, up-to-date and objective evidence to justify these figures.

There is a real fear that governments have taken them off the back of an envelope, inventing them for electoral advantage rather than deciding on them for the benefit of society, and young people, as a whole.

Who knows? The answer is that no one does until we hold a major and, above all, independent public inquiry to give us hard evidence in answer to two questions.

How many graduates do our economy and our society need for us to function properly? Graduates are an expensive commodity to produce. We have to be able to point to a clear need for every person who graduates.

At the same time they generate a significant amount of the country’s present and future national income. If they are crucial to our economic success they are equally important in fulfilling social needs. Without doctors, teachers, social workers, engineers and - dare I say it? - even lawyers, there is no civilised and caring society.

We already exercise some regulatory powers in deciding how many graduates there should be in some professions: medicine is a case in point. For such an expensive and important product it is bizarre that we have no hard, objective and non-political research into just how much of that product we need to produce as a society.

How many real jobs are there for graduates? Any inquiry needs to take account of another big factor: employability.

Tabloid coverage of degrees in equine and golf studies exaggerates the number of joke degree courses on offer, but at the moment many degree courses are consumer-driven: universities offer what the students wish to study. In turn, what the students wish to study is not infrequently at odds with what potential employers might wish them to have studied.

We do a dangerous thing if we encourage a young person to attend university for years, enlarge their expectations of earnings and employment status, and then turf them out carrying a huge debt to find they are over-qualified and fit only for relatively low-grade employment.

If we allow this to happen, and if word spreads on the street among young people, we will discourage huge numbers from applying for a degree course.

We will also produce a disaffected generation.

Of course, any national estimate of the number of jobs for graduates will need to be broken down by subject area, and will need to add on a significant figure for those who decide to work overseas or who decide simply not to use their degree. Yet given sufficient determination and resources, a reliable figure should really not be beyond the wit of man or woman.

The case for such an inquiry seems unanswerable. If its conclusions were to have credibility its members would need to be drawn not from the usual suspects, but from employers and academics of non-dogmatic status. It would need the time and the resources to do its job properly. It would need to cast its net wider than the UK.

It would also face two major problems. First, whatever its conclusions, they would prove a number of influential people wrong, be they those who argue for 30 per cent of young people going up to university or those who argue for 50 per cent. Secondly, it would require a real definition of what a degree was, and what it stood for.

This is a very difficult question and it is extraordinary that we do not have an answer to it.

Is a degree a qualification suitable for up to half the population? Or is it something that quite properly should be more elitist? To be effective an inquiry would need to be willing to be unpopular.

In the words of a well-known satirical magazine, it is time we knew.

Dr Martin Stephen is high master of Manchester grammar school and chairman of the Headmasters’ and Headmistresses’ Conference