I tried watching BBC's live video on my Dell laptop with 4 GB of RAM an Intel Core 2 CPU with a 3.06 Ghz clock speed and an Nvidia Quadro FX 770M display chip using a proxy server.
I ran two tests. For the first, the laptop was running several other applications and used over 3 GB of memory as shown here.
Note that I accessed the BBC stream through an English proxy server, which may have affected performance. (I used it only to write this review).