I think you could find that out by actually visiting an Exeter Open Day, and encouraging your DD to speak to current students, who are generally volunteers for Open Day duties at any university I’ve worked at.
And your opening post and thread title are just wrong: 30% is not “ mostly”. It means 70% of students come from State education.
But whether or not a student is State or paid-for educated might not be the crucial thing. It’s about parental support, and family culture. I was educated at a bog standard comprehensive (as Blair called them ), because my parents came from generations of public school education (prep and boarding), and Oxbridge universities. They wanted us to be more part of the community we lived in, but our family culture was quite different from the majority of my school friends. Because of the cultural and educational capital of several generations of elite education.
So the best things parents can do for their DC is encourage reading, books, familiarity with a wide range and style of cultural activity, of reaching beyond a consumerist lifestyle etc etc etc. A lot of what paying for education is paying for is not, as @Bell8484 assumes social “elevation” but cultural enrichment. You can do that without paying for a school to do it.
I think the OP needs to get over a clear case of reverse snobbery, and take her DD to Exeter - or Birmingham, or Bristol, or any of the “top tier” universities (they’re not top tier because of social class by the way) - to meet actual students and staff.