People do get caught for illegally downloading copyrighted material, as it is illegal (certainly in the UK and US anyway). People have been prosecuted for doing so.
The BPI and RIAA have mainly prosecuted mass file sharers, who are sharing music files in the hundreds, to the thousands over P2P networks. The idea is that by removing these file sharers from the network, there will be less and less music available. They just simply don't have sufficient resources to track down and prosecute all the individual users who only download, say, several songs a day using a P2P program.
But this doesn't mean that they do not intend to prosecute those who download music illegally. They comment that they won't hesitate to track down extreme users, who illegally download copyrighted material in large numbers.
http://support.microsoft.com/kb/315222