This, definitely.
A student like this will have not had the same chance to compare themselves with others like themselves as one in an academic PS, a grammar school, or a state school in an area of professional parents and gauge they could stand a chance too. Also, they will not have the background knowledge about it all.
Also this. Imagine growing up in a community decimated by Thatcher's destruction of industry, where families are on 2nd & 3rd generation of being unemployed. THEN a possible Oxbridge kid. How does that child visualise scaling those walls?
They often will have been given the impression through their lives that certain things aren’t for them. They may doubt they have any chance of getting in. It could feel like a massive presumption on their part, and the fear of failing could be huge because of a feeling of ‘who do you think you are?’
When I think back to the Head of this school, genuinely lovely guy, but in no way set up to deal with this student's needs.
It is up to teachers and heads to encourage a brilliant student like this, to get in touch with admissions at the good universities and check everything out. Some head teachers can be appalling in their lack of knowledge and lack of encouragement. It is as if they are either complacent and think it isn’t their business, or think that university applications to top/difficult places could be seen as elite and those places are ‘posh’/ taboo.