Our message is loud and unequivocal. Social class, gender and ethnic background have no place in selection. The only demand we make is that our students have talent.
If my message sounds unnecessarily strident it is because the results of the first-ever independent research on Oxbridge admissions, jointly funded with Oxford University, make it clear that this, above all else, is what state students need and want to be told.
For years, both universities have tried to attract talented students from an ever-wider spectrum of society. But research findings by the National Foundation for Educational Research on the factors that sway young people in state schools in their decision on whether to apply to Oxbridge, demonstrated a need for us to reassure state-school students.
Their overriding demand to us was: "Emphasise that state school pupils are not disadvantaged."
One of the most often quoted discouragements cited by students was that teachers questioned their ability to cope with what they saw as the social atmosphere they would encounter. As vice-chancellor of Cambridge, I want to be clear that the only elitism acceptable at Cambridge is academic excellence.
In universities, we are all conscious that teachers in schools have heavy demands on them. Here at Cambridge we already knew that teachers are crucial in both encouraging and discouraging young people from making an application to Cambridge.
Surprisingly though, the research showed that young men were more likely to have been encouraged to apply by their teachers. Overall, young men emerged as much more likely than young women to apply, a result we found surprising as 46 per cent of our applicants are women. It is our responsibility to ensure that teachers have accurate information about Cambridge to pass on to young people.
We've appointed a schools-liaison officer, produced our first teachers' booklet, which has been enthusiastically received, and approached every school with a sixth form in this country with a campaign "Put Yourself in the Picture", showing that students from all backgrounds fit in happily at Cambridge.
Two-thirds of teachers and lecturers believed the interview process, crucial to the Cambridge admissions system, disadvantaged their students.
I remain convinced the interview helps, rather than hinders, in drawing from a wider spectrum. Every applicant is seen by more than one person. Personal contact means interviewers can make allowances and spot potential. If Cambridge selected only on A-level grades, the approach would have to be more cautious and schools at the top of the league table would inevitably take the majority of places.
We have long had guidelines for interviewers but last year we issued a formal code to try to ensure widespread consistency. We're also issuing a booklet for candidates based on students' experiences of interviewers.
There was good news for us: young people recognise our academic excellence and are not put off by our earlier closing date or application form.
Our additional STEP exam taken by most students wanting to study mathematics has not proved a deterrent to the success of state school students; they win around 62 per cent of places in mathematics, the highest percentage of any subject taught at Cambridge.
But we still wrestle with perceptions. Some teachers thought that as few as 10 per cent of Cambridge students came from the state sector, when the figure has been around the 50-50 mark for some years now.
Comprehensive schoolteachers were more likely to believe it would cost a student more to study at Oxbridge, while in practice nearly all undergraduates live in college accommodation, only a bicycle is needed to get around town, and substantial hardship funds are available. Recent comparisons have shown that costs here are low and I am concerned that we should make more effort to put this across.
I will not consider the option of "dumbing down". We are looking for students with the ability to get the equivalent of three As at A-level. But we also know that some able students from disadvantaged backgrounds who have this potential to undertake our tough undergraduate courses, will probably not make these grades. Every Cambridge college takes part in a special access scheme to make realistic offers to such students.
We want bright young people from homes and schools with no Cambridge tradition to have the confidence to consider us; teachers can help by bolstering this feeling of confidence.
If young people make the choice to go elsewhere that is fair enough: but I would hope their decision is based on careful judgment, not on prejudice and false assumptions.
I am convinced that the measures we have already taken at Cambridge are on the right track, but this research project shows that we have much more to do if state school students and teachers are to believe our message.
Professor Sir Alec Broers is vice-chancellor of the University of Cambridge.