The British Phonographic Industry (BPI) has asked a number of the UK's biggest internet service providers to restrict access to Fenopy, H33t and Kickass Torrents.
The request to block the sites was made in a private letter which leaked last week, BBC News reports. According to the site, BT, Sky, Virgin Media, O2, EE and TalkTalkBT have indicated they will only comply if a court order is put in place.
A BPI spokesman said the three sites are profiting from illegally distributing copyrighted material in the same way The Pirate Bay was.
"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," they said.
"It is plain wrong. The existence of these sites damages the growth of Britain's burgeoning digital music sector."
The move is the BPI's second major assault on Torrent sites this year, following a High Court ruling in April which resulted in a number of ISPs restricting access to popular Torrent site The Pirate Bay.
Days after the block went into effect a Pirate Bay spokesperson reported that users had circumvented the block and the restriction had in fact 'increased site traffic'.