Fenopy, H33t and Kickass Torrents could be blocked in the UK before Christmas if the BPI successfully obtains a court order, BBC News reports.
The BPI claims that the three sites, which attract around 1 million monthly UK users, are distributing music and other media illegally.
BT, Sky, Virgin Media, O2, EE and TalkTalk have all been contacted by the BPI and ordered to block access to the offending services. The ISPs have allegedly said they will comply providing a court order is obtained.
Back in April, the BPI successfully had file-sharing website The Pirate Bay blocked by the UK's leading ISPs. However, critics point out that users can easily circumnavigate the ban using proxys and other methods.
"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 spokesperson.
"It is plain wrong. The existence of these sites damages the growth of Britain's burgeoning digital music sector."
According to web traffic figures from Nielsen, The Pirate Bay's UK visitor figures have dropped by three quarters since the ban came into effect.