Using google chrome on ubuntu 10.04, simply navigating to the following URL works for me:
http://mediaweb.musicradio.com/Show.asx?StreamID=2
Note: I have mplayer and vlc installed
If that doesn't work, their FAQ says: "If you are using the Linux Ubuntu operating system we recommend installing VLC player and then opening the following URL in VLC player to listen to Classic FM: http://mediaweb.musicradio.com/Show.asx?StreamID=2"
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