But as a head of department in a selective state school who has followed the progress of our own small cohort of four Oxbridge applicants, I realise I was rash in assuming the applications system was fair.

While I am in no position to measure Ms Spence’s suitability to study medicine, I know my own school’s candidates well enough to see that the offer of places in no way reflects their ability and potential.

Candidates 1 and 2 are as bright as the proverbial button. Their eyes light up as they latch on to an idea and develop it beyond all recognition. They take a nanosecond to understand a new concept and have a thirst for knowledge in the most unassuming way. Both work phenomenally hard, and I wish I knew how to stretch them even half fully. Neither was offered a place.

Candidates 3 and 4 are very able academically, but slapdash in their approach and nowhere near as intellectually accomplished as the other two. Both received offers conditional on A-level results.

While I am pleased for the two successful candidates, they are far less deserving of an Oxbridge place than their unsuccessful peers. Many factors, of course, come into play - choice, of course, of university (Cambridge is usually more difficult to get into), and of college.

These variables place students from major public schools at a huge advantage. Their teachers are paid to know which combination of university, course and college maximises each individual’s chances of acceptance. And for these students’ parents, the issue is not one of “we shall cross our Oxbridges when we come to them”, as author Jilly Cooper once wrote, but of going hell for leather for Oxbridge from the moment their child is born.

I do not deny that Oxbridge dons have a good idea of which candidates will do well, but I refuse to believe that they have much more than that. Oxbridge colleges are increasingly susceptible to the same pressures as other universities. For example, Oxford colleges hope to finish each academic year high up the Norrington Table. This measures its number of first, second and third-class degrees. So most tutors are under pressure to recruit students who will give their college the best chance of a high place in this exam table.

In the final year of my own course at an Oxford college (and yes, I did get in because my public school told me I didn’t have a cat in hell’s chance unless I applied to X college to read Y), 10 of us were due to sit finals. Eight achieved second-class honours, one got third-class honours, and the 10th student never finished the course.

Eight students with second-class honours from an original entry of 10 might not seem too bad, but it is unimpressive when you remember that dons stress they look for potential in applicants rather than evidence of having been taught well. The failure of 20 per cent of my peers to achieve a second-class honours degree proves that Oxford dons are as prone to human error as anyone else when it comes to spotting potential.

Given this, and that there are many more suitable applicants than places for most Oxbridge courses, I propose an alternative means of selection. Out-and-out geniuses are awarded a place automatically. The names of all other very able candidates go into a hat, and places are offered to those drawn out. Hardly scientific, but would this be any less fair than the present lottery for places?

Jenny Owl is a head of department in the north of England. She writes under a pseudonym