I started teaching in a big state grammar school that sent huge numbers to Oxbridge every year. They weren’t groomed either, but were formidably clever, the intellectual cream of a ferociously selective school. I changed sectors. In a former, newly independent, city grammar school, much smaller than my previous school, we couldn’t compete in numbers, but “obvious” Oxbridge candidates still tended to get in pretty safely. In preparation for “seventh term”, the post-A-level selection process, high-powered, inspiring teaching took candidates far beyond A-level. Here, traditionally academic schools gave their students an enormous advantage.

By the late 1980s, I was head of sixth form and preparing pupils for a very different Oxbridge system. Seventh-term application had gone at Cambridge (later at Oxford) and both universities started estimating candidates’

potential, rather than their previous attainment (they might argue that they always did).

Oxbridge entrance had changed, mostly for the better. Certainly, more can now realistically dream of the Dreaming Spires, but competition becomes more intense every year. It’s difficult to find extra time for Oxbridge preparation in the first term of a very pressured Year 13. In my school, some departments fix extra sessions with candidates, but lack of flexibility in the timetable since AS and A2 came along means these are usually at lunchtime. In other subjects teachers will routinely give their brightest students extra “extension” work. We offer a practice interview, usually with someone unknown to the candidates (such as a governor), and often share that service with a nearby comprehensive.

But it’s tough. Nowadays I tell Oxbridge applicants that they need to be brilliant and lucky. Still, every year, several strong candidates whom I am sure would have won a place years ago are disappointed. That’s the luck of the draw, perhaps. But these are students I know would thrive, academically and socially. Their rejection often seems unjust, despite our understanding of the nature of the competition. If we’re confident that Oxbridge really does base its decisions on candidates’ potential, there’s no cause for complaint. If more comprehensive school candidates are successful as a result, that’s great. I wish I felt confident.

I’ve never sensed any bias against my pupils because they come from a private school, but for two decades I have suspected that their pervasive West Midlands accent and natural reticence disadvantage them. But in dreaming up an image of the successful candidate (obviously a Southern smoothie), I’m probably as prejudiced as the tabloids that hurl invective at colleges that turn down a bright youngster from a northern comprehensive.

Oxford and Cambridge certainly interview and test far more rigorously than any other university. So if they are so certain about the efficacy of that process, do they really need to rely on A-level grades for the final sorting? Why say: “We think you’re good enough,” then snatch the place away when a candidate just misses that third A grade, often in a subject unrelated to their planned degree course? Is it because they can’t make their minds up, despite their vaunted selection system? Besides, grades are crude boundaries applied to bands of marks. Nowadays the actual A-level marks are published, so why don’t colleges require an overall mark in a subject, or a points total across all the subjects? Harsher, perhaps, and unforgiving - but more precise, less arbitrary.

If all those searching interviews and all that testing pre A-level still don’t provide enough information to make a decision, why not go further? Just look at A-level marks and take the top 200 candidates as a faculty, sharing them out among the colleges. Faculty-based selection would save candidates the lottery of picking colleges because they think they’re a Trinity or St John’s type - or because “maybe there won’t be too many trying for English there this year”. Oxbridge likes to have its port and drink it. Neither interview nor A grades are enough for Cambridge mathematics candidates: they have to get top grades in Step (sixth term examination paper) too. I’ve seen candidates notch up four A grades but lose their place because they “dropped” to a Step grade 2. Maths dons tell me the maths tripos is so tough that they need this extra discrimination or candidates just won’t cope at Cambridge.

Schools might wonder what ivory tower these people are locked in. Additional tests and top grade hurdles can only serve to disadvantage state school candidates, who are less likely than their independently educated rivals to get extra coaching for them. Why does Oxbridge not put its trust in its ability genuinely to gauge candidates’ potential pre A-level? After all, even the top universities are there to teach the raw material they admit. Or are they, in truth, prepared to take only candidates who are so bright that they don’t need to bother too much?

Bernard Trafford has been head of the independent Wolverhampton grammar school since 1990