Unable to find accommodation in Manchester

Hi!
I've been looking for accommodation for a while now, and haven't had much luck. I reach out to as many vacancies as possible, but haven't gotten any replies and I was stupid enough to not apply for uni accommodation earlier this year (I am a third year student at the University of Manchester who spent their first two years in halls). My only hope now is applying for uni accommodation again but I'm scared they'll turn me away too. Last year I applied for uni accommodation fairly late (mid-September), and was still able to get a room fairly easily, so that has been getting me going thus far. However I had a back up place last year, and this year I don't so I'm really scared.
When do you think it will be right for me to talk with the uni people? I reached them out via email on the 11th of September last year, and the next day they got back to me with an offer. Considering the deadline for first year accommodation is today, do you guys think emailing them again on Monday would be a good idea? I'm trying to think of the odds; there are probably thousands of rooms they have available, surely they must have a few dozen empty across all their halls. I have no preferences at all (something about how beggars can't be choosers), so I'm hopeful something works out. Have you guys tried this before?