In the recent Hoxton sale, they were offering £1 rooms right through August.
IMO, London hotels are far from sold out and prices can only fall in the coming weeks.
I've read this isn't unusual for Olympic host cities and the more I think about it, it doesn't surprise me in the least. I'd never take my wife and kids to see the "canoe sprint" let alone fly half way across the world to do it, but because it's here, I want to do it.
Very few events will surely attract the 'pay anything' brigade. 100m finals and the like maybe, but elsewhere you've presumably got locals (incl. 'near Euorpe') and contestant friends & families. I may have to stay in London during week 1 but I'm not sweating it (and worst case scenario I can be home in 90 mins...)