If the light comes on to show that your hard drive is a running whenever the problem occurs it would suggest that your computer is low on RAM. Apart from ensuring that no unnecessary programs are running (or, of course, installing additional RAM) there's nothing that you can do about it.
If the hard drive light doesn't come on then it's likely that your internet connection hasn't got sufficient capacity to handle both downloads (i.e. the music file and the web page information) simultaneously. Check your download speed here:
http://www.bbc.co.uk/iplayer/diagnostics
and here:
http://www.speedtest.net/
My own download speed seems to be slower than usual tonight. (It's running at about 7Mbps instead of the usual 10.5Mbps that I get). Perhaps there's a problem with the 'backbone' of UK internet services?