Approximately seven out of ten Oxford undergraduates went to a State school. Ethnic minority membership of the student body is above the percentage of ethnic minority people in the 18 to 25 year age group nationally.
It appears that access to all Russell Group Universities is dominated by pupils from the south east of England (both State and private), but, if you obtained a place at Oxford, you wouldn't be the only Northerner in your college. It may be worth adding that Queen's traditionally has a Northern vibe, and that St Peter's has a Merseyside vibe.
If you are a keen clubber, and run out of options at Oxford, you can always get the Oxford Tube - a 24/7 bus service to and from London with wifi, aircon, and seats to fall asleep in. It's fast in the dead of night, and slower during the day (traffic on the Westway).