The UK's six biggest internet service providers (ISPs) have been asked to block three more file-sharing sites from their customers: Fenopy, h33t and Kick Ass Torrents.
The UK record industry trade association, the British Phonographic Industry (BPI), has sent letters to Sky, BT, EE, TalkTalk, Telefonica and Virgin Media, with the blocking request.
This follows the BPI's success in April in getting the same six ISPs to block the Pirate Bay.
"Like the Pirate Bay, these websites are profiting illegally from distributing music that isn't theirs, without permission and without paying a penny to the musicians, writers and producers who created it," said a BPI spokesman.
"The existence of these sites damages the growth of Britain's burgeoning digital music sector. We have therefore asked Britain's six biggest ISPs to block access to the sites."
The BPI said it is up to the ISPs to decide whether they block the sites. However, if the ISPs refuse to block voluntarily, then the BPI will consider seeking a court order.
A TalkTalk spokesman said in response that it would only block websites when ordered to do so by court.
"If the BPI gets a court order we will, of course, comply with the law," said the spokesman.
BT has said it is currently considering its options.
Meanwhile a Virgin Media spokesperson said, "As a responsible ISP, Virgin Media complies with court orders addressed to the company, but strongly believes that changing consumer behaviour to tackle copyright infringement also needs compelling legal alternatives to give consumers access to great content at the right price."
The Open Rights Group has long been campaigning against putting restrictions on ISPs, in an argument to keep the internet free and open.
"I expect this [blocking] will go ahead, although whether this is a good idea or not is another question," said Jim Killock, executive director of the Open Rights Group, in an interview with V3.
"What you can see is the BPI speeding the process up. Now it is trying to block three sites at once. It's disturbing. It's important that the courts look at this carefully."
"When you censor a whole site, you move away from copyright enforcement into the realm of censorship."
The BPI won a landmark case in 2011 under the Copyright, Designs and Patents Act to be able to block websites when it went after the Newzbin 2 website.
Since then it has moved to attempt to block other sites using the ruling as a precedent.
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