After all that work the problem seems to have magically resolved itself only moments after I posted this.
I wish I knew what I had done to fix it, but the things I actually tried seemed to have very little affect on it.
edit: ...and it's back again. I've figured out the trigger at least, it's a specific video.
Okay the problem seems to be something in the relationship between firefox and silverlight. I was finally able to get silverlight to load again after forcing it in chrome several times. Everything seems back to normal for now. I suggest nobody attempt to watch top gear uk S7 e7 in the meantime. Something is broken with it and it seems to cause this problem.