More rich students go to state schools than private schools - this is true for every income decile. So if wealth equates to getting into Oxbridge you wld expect a higher %. (I don’t necessarily think it does but some on this thread do.)
Also, the Oxbridge figures use the school type at the application stage not the school
type at GCSE (although as noted above this can be taken into consideration when deciding whether to make an offer). So there will be students classified as state who only went to state school in the 6th form.
There will also be students who appear to be from state but are actually educated in their A level subject(s) at private schools (especially when it comes to classics which is where this thread started!).
This obsession with state vs private is a poor proxy for family wealth, quality/experience of school or privilege/depravation. Whilst we obsess about that, overseas applicants are besting our best students from both sectors - especially in STEM. That should be concerning us all, and especially the govt.