That's likely to depend hugely on the subject. I'm privately educated in relevant subjects, and went on to do an engineering degree at a well-regarded universit

That's likely to depend hugely on the subject. I'm privately educated in relevant subjects, and went on to do an engineering degree at a well-regarded university (not Oxbridge, but ranked with them), but there's just no way I had the technical chops at the time to get past these questions. I don't think I'd even read GEB yet. With a technical subject, it's relatively straightforward to put a meritocratic admissions system in place. I don't think you can make that argument for humanities subjects.