Officer Kite,
I did enrol well in advance (six months ahead) last year and they did say they were very short on accomodation but I've paid for it. The bloke mentioned something about a chance that we would end up in hotels for a bit. Maybe I just got in before they ran out.
I have been in previous accomodation shortages like this before with my old employer and they worked it out well. You think they would just rent several houses then charge the standard rate on their website, they would turn a half decent profit as well! But I am not up to speed with UK rental law maybe thats a no-no! Good luck!