Classic FM uses FlashPlayer:
http://www.classicfm.co.uk/on-air/ways-of-listening/how-listen-classic-fm-online -radio/
(scroll down for info on listening with a Mac).
You do of course have to sign up with them.
The latest version of Adobe FlashPlayer can be obtained from here:
http://www.adobe.com/shockwave/download/download.cgi?P1ProdVersion=ShockwaveFlash
(You can check here:
http://www.adobe.com/products/flash/about/ to see which version you should install for your Mac and OS.
You should first uninstall any previous version of Flash Player, using the uninstaller from here (make sure you use the correct one!):
http://kb.adobe.com/selfservice/viewContent.do?externalId=tn_14157
and also that you follow the instructions closely, such as closing ALL applications first before installing. You
must also carry out a permission repair after installing anything from Adobe.
You should also ensure that you have downloaded and installed the correct version for your Mac of
Security Update 2009-001 (and for Tiger only, 2009-002 and 003).
(N.B. Security Updates require both a restart and a permission repair.)