I'll explain this fully. This is for first year undergraduates:
When you apply, you will be put into one of 4 groups, as stated by the Principals of Allocation
1) Medical requirements
2) Firm Warwick and apply before 31st July
3) Insure Warwick and apply before 31st July
4) Apply on or after 1st August
At the moment, groups 1 and 2 are more or less guaranteed a place on campus. Perhaps there are enough spaces on campus for group 3, but lets say for example there are not. If there are too many people in group 3 for places remaining on campus, a random ballot is then drawn. If you are lucky then you will be offered a place on campus. If you are unlucky then the uni will assist you in finding a place off campus. This can often be at university managed accommodation.
Now, if you are in group 3 and get a place on campus, it is still possible to be allocated a single room (some people have managed to get AV). This group will first fill up undersubscribed halls, possibly Rootes and Westwood and any halls where people drop out in September, for example. IF you are allocated in Westwood, you can still be allocated a single or shared room. If you get placed in a shared room, this is ususally temporary and one of the two people will have to move out in the first 4 weeks, either off campus or to empty rooms on campus (again, people drop out). After the first few weeks, you should all be in single rooms.
The only exception to this is Benefactors sharing. But then again you applied to a shared hall
Last point: Westwood rooms are the largest on campus, so it won't be that cramped. You also only have to pay half the rent.