When I talk to the students who have made it to Cambridge, they see their admissions interview as having been make-or-break: the point at which the value of their school career and their future prospects are determined.

That myth – and it is a myth – is shared in the outside world. There’s an extra layer of miscomprehension, based around the image of dons asking abstruse questions designed to weed out inexperienced state school students and guarantee that busloads of men from Eton arrive the following autumn.

But it is true that Cambridge still has its work cut out to convince the outside world that it is open to everyone with the right talent, irrespective of their background. We have to attract potential students from all over the UK, instead of the current over-concentration of applicants from south-east England.

Each year, as master of Selwyn College, I sit in on some of the Cambridge interviews and decisions meetings. What I have seen is radically different from the image constructed by our critics. The much-attacked interviews are only a small part of the selection process and their importance has diminished.

Interviews may well have once been the thing that mattered – agreeable chaps selecting agreeable chaps. But for an academic choosing the next cohort for their subject, there is now a vast amount of data, ranging from the student’s GCSE and admissions test scores (introduced to add hard evidence since the demise of AS modules), through to the school’s assessment of suitability for a degree course and their grade predictions. Some students are deselected before they get to an interview, if their record or predictions aren’t strong enough; and even the most brilliant interview will not secure a place if the rest of their profile is below the par of the field. 

In the overwhelming majority of cases, offers are also conditional on the A-Level or equivalent results. Sometimes this is overtly a tough offer, because we want a student to show they can work hard and deliver an outcome at the top end of expectations. So the majority of places aren’t finally decided until eight months after the interviews.

But unlike many other universities, interviews are still part of the process, and discussion of the Oxbridge admissions process, rightly, includes questioning whether it’s a level playing field for people from all social and educational backgrounds. We now have multiple mitigations, in an attempt to ensure that private schools can’t simply coach their students through the process. We offer interview advice to state schools. We do workshops in our outreach areas.

Crucially, in my experience, we also ensure that the questions are fair to everyone, and are not items of Oxbridge whimsy. This year, I witnessed medicine interviews, where candidates were asked to work through a practical human biology question of the kind they would have been familiar with at A-Level: the key thing is to see their mind working through the problem, not whether they get a right or wrong answer. Then they were asked about their understanding of consent when a patient is receiving treatment, which seems like a reasonable thing to ask a prospective doctor. Interviewers receive unconscious bias training to help them assess candidates fairly. 

Selectors have access to other important data. We know if a student is doing particularly well as an individual within a low-performing school – a significant plus sign – and we can also see if they come from a postcode with a poor rate of participation in higher education. Therefore when our critics say we should consider contextualised admissions: we do already. If you are a high-achieving student from a tough school in an inner city, or from a rural school with a challenging catchment area, our selectors will want to admit you.

I saw that when I dropped by at the winter “pool” at the start of January. The pool is the system by which offers are evened up across the university, and it brings scores of academics to a set of rooms – this year taking over much of the ground floor of Newnham College – where in the current round, 4,500 application files were available for their consideration. A college will put some of its potential offer candidates into a selection involving all the colleges to test that they are getting the best available. The pool is also used to ensure that strong candidates still get a place, even if their first-choice college is oversubscribed.

Rightly, all those academics rifling through the files have targets set by the university, and agreed by the Office for Fair Access (now the Office for Students), for state school numbers; and for candidates from poorer areas, and we routinely meet or exceed them. The Cambridge target for 2017 was 62-64 per cent for state school admissions, and in the last few years the numbers have consistently risen and are getting close to two-thirds of the UK cohort. Yes, some do come from grammar schools, but at my own college 36 of this year’s intake were from comprehensives – compared with 30 new students from the independent sector. We also have a target that 13 per cent of admissions should be from neighbourhoods with low participation rates in higher education – and Selwyn came in last year at 14.7 per cent. Meanwhile, 22 per cent of home undergraduates are now from ethnic minorities.

But we can only select from the people who’ve applied. The Sutton Trust has done some valuable research that shows that 40 per cent of state school teachers wouldn’t advise their brightest students to apply to Oxbridge, and part of that may be fuelled by misconceptions about their likely success rate, as well as outdated images of what the universities are like.

The one caveat is that selectors have to be confident that students can cope with the course: Cambridge undergraduate courses are demanding. We’re certainly keen to address some of the gaps in school attainment through transition years, which will invite students who may not have had the academic opportunities available to others to apply for a year-long course to prepare them for Cambridge entry standards. Work is going on to introduce transition years from 2021.

I’m happy for the pressure to be maintained on Oxford and Cambridge for them to be open to the brightest talent and to be more representative of Britain in the 21st century, and the statistics are proving that it is happening albeit with further to go.

But it cannot be achieved in a flash – and some of the bureaucratic and political interventions are counterproductive if they think the answer is to lower standards. We have the students already who show that it’s possible to succeed at Oxbridge whatever your ethnic, class or financial background – and they and the next generations will offer the proof that the ancient universities are changing with the times.