The reason that Youtube is okay is that the Video quality is much lower and therefore each video frame is a lot less bits.
What happens is that when you view a BBC video, if buffers up some of the data before it starts. Because it takes 1/3 of a second, (300 Ms), for each packet of data, about 12000 bits, to get to your PC, the buffer will empty and you will get interuptions.
Could be QoS as one poster suggested. May be your ISP is poor. I get about 60Ms ping to
www.bbc.co.uk on a 3 MBs connection.
QoS is designed to some types of network traffic to jump the queue. It is there to allow real time (Video/Voice) traffic to flow smoothly and not be interupted when stuff like Microsoft patches are being down loaded. I've never looked at QoS on a PC but you may need to configure it for the BBC.
You could try pausing the playback and going for a cup of tea. This will allow the buffer time fo fill up.
Hope this helps.