After adding the station in Music > New Internet Radio Station, and trying to play it,
Rhythmbox should prompt you to install the necessary packages. This is what happened for me and then 6Music played.
If Rhythmbox doesn't prompt you to install the necessary packages, I got 6Music playing by installing the following additional packages on 12.04- the packages names might differ on 12.10. This is the list that
Rhythmbox recommended, but not all are probably necessary:
sudo apt-get install libcdaudio1 libflite1 libgme0 libgstreamer-plugins-bad0.10-0 libmimic0 libofa0 libopenspc0 libslv2-9 libspandsp2 libvo-aacenc0 libvo-amrwbenc0 libwildmidi-config libwildmidi1 libzbar0 gstreamer0.10-plugins-bad
gstreamer plugins are probably the most important, but installing the whole lot of recommended packages did get 6Music streaming.