Research for an educational charity suggests bright state school children are under-represented at the UK's top universities.
"You will find a niche," says Tristan
The Sutton Trust says the main reason is that not many state-school students apply to leading universities.
They are often held back by the low expectations of their teachers or a lack of aspiration in their family, it says.
Sutton Trust chairman Sir Peter Lampl said a survey of state school teachers found 80% thought their pupils might not be happy at some of the top universities.
Oxford physics student Tristan West, 21, was one of very few pupils to go from his South Wales school to Oxbridge.
"When I arrived at the reception of Merton College for my interview, a student took me to a room where I was going to stay for the night," he told the BBC News website.
"The student came out and put on his leather driving gloves and I thought: 'What am I letting myself in for?'"
A feeling of being in the wrong place stayed with him during his two interviews with tutors the next day.
You think 'it's not Rory from Eton, it's just Rory'
Despite a lot of self-driven "reading around subject", he wasn't prepared for the Oxford interview experience.
"I had had just one mock interview at my school as preparation, plus a short chat with a retired Oxbridge don my mother had met through church.
"I think I completely flunked the interview and that a maths test I had done in the morning got me through.
"I was slightly taken back at the interview, because there was not much of a warm up; just a 'hello, you're Tristan', then it was 'what do you know about physics?'".
"I mentioned something about gravity, then they gave me a written problem and I felt flummoxed by it. But they were more interested in how I reacted to it rather than my getting the answer.
"I came out of the interview thinking 'Why did I come here?"
So when he returned home after a Christmas holiday to find a letter offering him a place, he was staggered.
"I thought 'What on earth are they thinking of?' But we were all really chuffed. My parents, my sister and uncles and aunts, everyone was thrilled."
Drive to achieve
Tristan says his parents had always encouraged him to aim high.
When he was at school his father was working in the mines as an electrical engineer while also studying for a degree through the Open University.
His mother was a teacher, who also gained a degree through the OU.
"I always had a good head for the academic stuff in school and had some kind of drive to be the best and go for the best. I wonder if my parents instilled it in me from a young age?
"They told me how important it was to get a good education and a degree."
Tristan's school - Ysgol Gyfun Llanhari - in the town of Llanhari, Rhondda Cynon Taff, did not have big tradition of sending students to Oxbridge and there were no special lessons for people applying there.
Sutton Trust says pupils are often held back by low expectations
"I was the only person to get to Oxford from there in three or four years, though I was part of a good cohort of about 10 that year who went to top universities.
"They were thrilled that I wanted to do it, but there wasn't much extra support available. They were more interested in getting people into any university or higher education."
Arriving at Merton College three years ago (he is about to start his fourth and final year), he says it did not take long for him to feel he belonged there "as much as anyone".
"Initially, you notice everyone's background, but after a week or so, it didn't matter at all. You think 'it's not Rory from Eton, it's just Rory'.
"At our college, it is about 50-50 independent to state school, but you just really don't notice. Other people are just like me. It just seems as if everybody fits in quite well."
Tristan has been involved with college initiatives designed to encourage more applicants from state school pupils.
He has written an alternative prospectus for the college, showing what life is like in the college, which is sent to secondary schools.
And he has acted as a guide on the college's Open Days for schools and on university-wide Open Days.
He has this message for teenagers thinking of higher education: "I would say apply to wherever you want to go - you will fit in wherever you go.
"In a group of thousands of students, you are bound to find many you get on with."
"You will find a niche. You may as well try; you have nothing to lose and if you succeed - brilliant!
"You have just as much right to be there as anybody else."