The biggest problem is the fact that music rights are sold separately in each European country, and collecting societies - various groups which collect copyright-related fees and give them to the artists - have different contracts that allow artists to collect payments only from an agency based in their country. This is what's stopping Apple from offering iTunes in some European countries; if they were able to set up a single store for all of Europe, it'd be much easier.
Now, EU Competition Commissioner Neelie Kroes has urged the music industry "to move quickly to adapt their licensing solutions to the online environment." It's not just a friendly nudge, though. The European Commission said the same thing last July, and found 24 European collecting societies in violation of EU antitrust rules. If things don't improve, the EU commission has the power to start imposing fines, and - as we know from the examples of Intel and Microsoft - they do it with a heavy hand.