Well I didn't have any problems at all.
I didn't go to the student accomodation office, I just sorted myself out from the list of local accomodation, which was available from the civil aviation department's office.
That way you aren't 'competing' with loads of other students, just joe public. There was plenty of space within walking distance of tower hill.
I assume they still keep a list.
If so, GET IT!
IH