In reply to Philip: many years ago... students mostly lived in Portswood, especially in an area called the avenues (there's a load of roads called such and such avenue, all parallel, south of the university if you look at a map you'll see). It isn't far to campus, has shops, takeaways and several of the popular student pubs in easy reach. Highfield is closer to campus and was regarded as a bit nicer. Obviously nicer or cheaper houses could be found in both.
I lived in Shirley which is on the far side of the common, which makes a pleasant walk or cycle ride there and back but is quite far and very indirect by public transport, it wasn't at all a studenty area at that time. Then I lived in Bitterne which is also not studenty, close to a park and quite nice. Basically the university is next to the common on its west side, areas south and east (Portswood and down to the river respectively) were popular and north (Flowers estate) was not, relatively nice or grotty houses were available in all the areas. My only subsequent visit a couple of years ago suggests things haven't greatly changed.
When I was there, there was indeed a housing office and they did actually publish a list of people looking for extras about this time of year. That would definitely be my first port of call. University oriented landlords would advertise on it but typically you needed to get a whole house and have the right number of people, now there will be people looking to fill a space. Obviously it is much easier if you are there in person and if I were in that situation I would probably go and poke about the union and look at the notice boards of (sports) clubs or departments that interest me and see if there were small ads, or if they have webpages with a chatpage as that might be a shortcut to meeting some like-minded people.