I can only speak for Wycombe Air Centre. Extremely professional and friendly bunch. Wycombe Air Park is also well run by the very good ATC, so a good, controlled atmosphere to learn in. Wycombe have mainly Cessnas (high wing). I think that they have got rid of their low wing Piper but I'm not sure.
I don't know the Oxford based school, but why don't you have a lesson with each and see how you get on. The time will all count towards your PPL.