To fetch BBC iPlayer content there's a utility called get-iplayer. This turns out to be a monolithic Perl script - yuk - but I don't feel like re-implementing it, so I guess I'll have to wrap it up somehow. The Debian package installs and runs OK on this board.
It seems that several versions of the videos are available in different formats. Previously the versions intended for the iPhone were most useful as they were MPEG-4 files downloaded over HTTP. But the BBC now restrict those files to devices with a particular SSL client certificate. Maybe that certificate can be extracted from a cracked iPhone, but I've not investigated that yet. So instead we can download Flash video over RTMP. This Flash video is apparently MPEG-4 AVC aka h.264 with AAC audio in a Flash container. For extra confusion there are two kinds of flash video container, FLV and F4V, and this is the older FLV. The container format is specified here. Hopefully once I can extract it from the container, it will be understood by the hardware decoder. So far I've not found a simple library to do this extraction, so I may have to do it myself.