In a collegiate system we should hope that the JCR is the main 'go-to' body for students. However, despite the general autonomy of the JCR, a lot of University-wide, joined-up thinking goes on. The university's student union, OUSU, provides support on issues effecting the whole Oxford University student body: Improving the quality of private student housing in Oxford and creating a structure which holds landlords more accountable is a major focus this year, for example. As individual members of the university each student is a member of OUSU and so can get involved in any of OUSU's campaigns and use all of OUSU's support services. Check out their website (linked above) for various welfare, academic affairs and more general student resources.
Trinity's JCR External Affairs Rep attends bi-weekly OUSU council meetings at which OUSU policy is decided. To have your opinion put forward at these meetings get in touch with the External Affairs Rep. To see what previous and upcoming council meetings have dealt with, have a look at the OUSU Council webpage.