When this thread started, the BBC test page was working for me.
But now it isn't! Nor other BBC videos :( Though all three of the quirksmode videos still work, as does youtube. So it's definitely a BBC problem.
What I have noticed is that if you right-click on the misbehaving BBC video, it pops up a panel with some error diagnostics. Sadly, it seems to be one of those annoying windows that won't let you select the text! The pointer changes to a hand but doesn't seem to let you do anything.
There's some sort of dotted number - a version number perhaps? There's a list of errors, like bitrate and dimensions. And there's "Error: 4999"
So I hope that somebody at the BBC is reading this.