UK record lobby wants Pirate Party to shut down its Pirate Bay proxy

The BPI — the UK version of the RIAA — got the courts to order the UK's ISPs to censor requests to The Pirate Bay. The UK Pirate Party set up a proxy in anticipation of the order. Now the BPI has demanded that they shut it down. Word is that the news of the national censorship of TPB drove titanic amounts of UK traffic to the site. Will the current round do the same?