As far as copyright goes, the DMCA (ironically) provides a huge protection to American hosting companies as it specifically grants them shelter from copyright-infringement suits as long as they comply with any 'takedown' notices sent by the copyright holder. I'm not sure if the EUCD offers any similar protection.
Of course, there are complexities to the issue. Firstly that some media firms fire-off takedown notices indiscriminately (Verizon is noteworthy for this transgression), and while it is a criminal offence to file a takedown notice for material whose copyright you do not hold, the chances of Verizon being prosecuted for their over-zealous activity is negligible. Secondly, the site has to be careful that it doesn't run afoul of the charge of contributory infringement (as set out in the Grokster judgement), which was the main threat several months back when there was a lot of talk of media firms trying to work out a way to sue YouTube after the Google buyout.
The example you give is unique to the idiotic nature of the UK's libel laws, which need a thorough overhaul.