Last Thursday was deadline day for applying to study at Oxford and Cambridge. Each applicant will face the daunting prospect of a grilling by some of the world’s most formidable academics, within the ivory towers and grand surroundings that will feel familiar only to those who attend the country’s top private schools.

It’s an intimidating process for any 18-year-old, undoubtedly, and that’s before you consider the fact that successful applicants must not only ace their interview but also secure the stellar grades needed to actually take up their place.

Only the best prepared will succeed - academically, of course, but also in terms of having the experience and confidence to perform at their best in the intense atmosphere and unnerving surroundings.

With that in mind, it’s little wonder that statistics continue to point to a considerable under-representation of state school students at Oxbridge.

The Sutton Trust has found that independent school students are more than twice as likely as those from comprehensive schools or academies to be accepted to one of the 30 most highly selective universities. And, according to Professor Becky Francis and Dr Billy Wong of King’s College London, private school pupils are more than 55 times more likely to be accepted to Oxbridge than state school students who receive free school meals.

In this country, approximately 7 per cent of children attend private schools. Yet, in 2014, the University of Oxford awarded 43.7 per cent of its places to applicants from independent schools. Perhaps most alarmingly, a Sutton Trust report from last year shows that five top independent schools send as many pupils to Oxford and Cambridge as 1,800 state schools put together.

This is not a new phenomenon. It is perhaps extraordinary that the 1852 Royal Commissions on Oxford and Cambridge identified access by poorer students as a pressing issue that both universities needed to address.

Of course, the situation has improved somewhat since then. More than half of students at both institutions now come from state schools, and every college now appoints “access” students with the objective of encouraging young people from “non-Oxbridge backgrounds” to apply. But much, much more needs to be done before entrance is truly representative and fair.

The obvious place to start is the quality of our state schools, and here progress is clearly being made. This government has made education a key priority, investing in academies and free schools, driving up standards and increasing parent choice to help students from non-fee-paying schools to achieve the best grades they can.

But as we know, exam results are only part of what it takes to get in. So what else should we be doing to level the playing field? What is the X factor that a higher proportion of privately educated applicants seem to possess?

I strongly believe it to be both a confidence issue and an aspiration issue. Having the nerve to even apply is itself an indicator of background and expectations. Students educated in a school that prides itself on successful Oxbridge candidates are far more likely to take it as their right to apply. They will have been taught what is possible and thus their aspirations will have been raised. As well as possessing more self-confidence when entering the type of grand buildings that Oxford and Cambridge colleges share with the likes of Eton, Winchester and Harrow, these young people are also more likely to get the general and specialist tuition to impress the interviewer.

Small wonder that extensive research on this topic has repeatedly found that “fear of not fitting in” is a powerful deterrent to state school applicants. Even 163 years on from the Royal Commission, an Ipsos-Mori Omnibus survey of 11- to 16-year-olds still shows that 27 per cent of respondents indicate that “elite” universities “are not for people like me”.

This fear of applying to top universities - and, more generally, a lack of confidence and feeling of being able to pursue their dreams - is a dangerous barrier that holds back the potential of this country and the many young people in it. It’s up to all of us to take action, whether educated in the state sector, as I was, or privately.

But how do we confront a challenge that’s been around for centuries? I believe that inspiration is the key, and, more specifically, ensuring students in state schools have the same access to inspirational people that their privately educated peers can take for granted.

Speakers for Schools, the charity of which I am chairman, was founded to do just that. The organisation provides state secondary schools and colleges with talks from a range of industry-leading professionals, public figures and academics - free of charge. We currently have nearly 1,000 speakers signed up, from Nobel Prize-winning scientists to newspaper editors, sporting legends and business chief executives. Each of these renowned leaders gives their time to visit state schools to speak to students about their career and experiences.

Take renowned mathematician and TV presenter Marcus du Sautoy - one of our speakers, and someone who brings maths to life in a way many wouldn’t think possible. Du Sautoy attended a comprehensive school before going to Oxford, and is now one of the most respected academics in the country. There is no such thing as a university that’s “not for the likes of us”, and giving students the chance to hear from speakers like du Sautoy proves it.

But it’s not just about following in a role model’s footsteps - it’s about giving every young man and woman an insight into the world beyond school. Whether it be through a charity initiative, excellent career advice or an incredible school trip, the vital thing is to spark an interest. To convince all our students that everyone has the right and ability to follow their dreams - whether that be going to Oxbridge or doing something totally different.

Andrew Law is chairman of the board of trustees of Speakers for Schools, and chairman and chief executive of Caxton Associates