Ah, let me guess… You’ve got one of this swish newer generation iThings that support mirroring everything, even over Airplay, and all that jazzy stuff?
For older (ie 2010) devices and for the VGA/composite outputs, I believe it’s got to be supported on a per-app basis. Safari supports it, so if I use the iPlayer web version it works. But then I won’t get offline viewing. (Though I’ll admit I haven’t tested iPlayer 2.0 with composite so maybe they’ve sneaked in support unannounced.)
Perhaps the BBC just assumes we’ll all get newer iPhones soon. (And all TVs will have HDMI as well…)