I'd say Josephine Butler has a good mix and they will prioritise a student's finances when considering applications to remain in college for 2nd and 3rd years (as generally cheaper than living out).
Having said that, I ended up in St John's and yes, as a Comprehensive-educated person from a small Northern town, I am definitely in the minority but it hasn't mattered at all. It's a really friendly, welcoming college and I've enjoyed meeting people from different backgrounds to the one I grew up in.