I know it's not ideal and just means paying more money out on hotels Ana, but have you tried going to a few different parts of town? I was always busy in Angel, Waterloo, Victoria/Pimlico and there used to be quite a few of the OK hotels on the day rooms sites. It's fine over here in the City too, but again I know the hotel costs are horrific.
A bit off topic but I checked one of the nice hotels I used to work from and usually paid between £130 and £180-£200 for the night before the Queen's funeral, and the cheapest rooms (which weren't great and I didn't book them) were £999 
Amy, I thought you made a typing mistake when you said that the cheapest room before the Queen's funeral were £999 (£99 instead of £999)

Hope they put it back to a more normal price now

hotel prices are absolutely insane especially compared to last year at the same time.
And yes I've tried different part of town with dayuse rooms (City a few time, Tower Hill, Euston) and it hasn't been successful at all so far (one or two 30mins booking at most), I mean really not worth the hotel price + travel time. I will keep trying though and let's see what will happen