Nope, you are not stuffed.
I got into trent as an insurance choice, and was in the same position as you guys! People will drop out, not make the grades or just simply decide not to go, so spaces in uni ran halls do open up. The way it worked for me, (and you assuming it hasn't changed) is as as soon as I knew I missed out on my firm, ring up NTU accomodation and ask what places they have. Prepare and have a list drawn up of options. The line gets rammed, it took me 40 mins of solid ringing to get through!
Nottingham also has loads of private halls, which are also completly full of students (mostly freshers) such as goldsmith court or glasshouse which you could ring up and ask about places.
Hope this helps!
P.S. In my opinion, avoid Blenheim halls (where I got, not great and its 15 mins away up a huge hill, and I mean huge). Any other questions?