For the University of Oxford or Oxford Brookes University...?
For the former, students will (in pretty much every case I can see) live in college for their first year. I'm not sure the method by which students are "allocated" rooms (you may be able to indicate a preference for a higher or lower rent room, which will correspondingly be larger/nicer or more average usually) as I think it varies between colleges anyway. However regardless of this format, all students will be able to take up a room in college in the first year, as far as I can tell - whether this can be continued throughout the course or if they have to "live out" in second/other years seems to vary.
At Oxford Brookes, I don't know but I assume it's similar to other universities where after you'll apply for halls of residence after you accept and achieve their offer (this applies to an extent to Oxford as well - you will make any indication of preferences in accommodation after results, normally). Typically students look for private accommodation after first year, although you can apply for halls again normally (often priority is given to mature students and international students in this case).