You would need a programme like LP Recorder which is what I use for recording streaming audio. Get it from click here and while you are on there get LP Ripper as well. Obviously there will be lots of others but these two are the ones I use and I have never had a problem with them.
leo49, just tried the free version again now and yes, brilliant, need to make sure it is set to "Stereomix" then click on start and off you go. I did find the recording volume is always in the "red" but when I played it back it was perfect.
So, Kitz E Kat try Jetaudio I think you will find it is just what you want.