I think there are 2 reasons videos from the BBC don't load.

The first, which I'm almost certain stops the loading, is having your Flash privacy settings to never store any information. I have mine set to ask me when a new site wants to store information, but I can't set it to "No. Don't ask me again" on the BBC because if I do then the videos never load. I have to hit the "Deny" button when it prompts me, which it does, annoyingly, multiple times throughout a single video.

The second possible reason could be blocking of ad servers, but I'm not sure about this one.

Nope. Me too. I usually just search Youtube for the same headline and a video usually turns up. I don't know who the spammer is who does it, but I'm grateful.

Me three.