Just to share on my case:)
I guess I am considered late to apply for on-campus accommodation, I think I applied it on the information day of Nottingham on 13th August. I was really anxious that time, as I was told by my friend who has submitted her application months ago that she did not get a single and was offered her third choice which is shared room.
I was really really disappointed by that, as I was really really hoping for a single room, lol. So I asked my dad to fetch me to the uni itself on its info day, and it happened that there's a accommodation booth there. So I dropped by, asked the person-in-charged ( I think he's a student helper there) if there's any single room left, begging him to help me in every possible ways.
So what he did was, rang up the accommodation office and said " hey I have a student here who's looking for a single room, is it any available still? If there's, she will be making the payment right away" And of course what I got was a positive answer

Yay, really thrilled, got offer single ensuite bathroom and am alocated to langkawi hall.
So my advice to other students who really really looking for a single room or your first choice, you can probably drop by the office itself if possible, and bring along your parents if can, I guess that'd be more efficient in getting your problems solved.
*Just sharing*