I had the same problem. I used to be able to just press play. But then somthing unrelated happen to my PC and then I had to download real player.
I'm not a big fan of real player because it likes to take over every media file I have got and becomes the default media player. So what I did was to download the most basic free version. I chose the advanced install method (so I could choose my own prefrences) basically I unticked every box.
Now Real player sits in the background and behaves itself and I can listen to bbc radio.
And yes, it is strange how different bbc programs need real player but others do not.
which has all the codecs etc of Real player but uses media player 6.4 to run which is a lot less intensive etc... It's fantastic and I can uninstall real player and forget about it! there are also versions of quicktime which just installs the codecs etc and everything should then run fine. Give it a go and be impressed by it,