The recorded music industry's trade group has asked internet service providers (ISPs) to freeze the accounts of customers who illegally fileshare.
The British Phonographic Industry (BPI) has written to Tiscali and Cable & Wireless asking them to suspend 59 accounts for "illegal filesharing".
Until now, the BPI has focused on individuals, rather than other firms.
The ISPs should now "put their houses in order and pull the plug on these people", said the BPI.
The internet has made it far easier for people to share music files and thus to breach copyright.
The BPI says this latest move will enable the record industry "to deal with a greater volume of cases more quickly and efficiently".
BPI has identified 17 Tiscali IP addresses and 42 Cable & Wireless IP addresses which were used to upload "significant quantities of music owned by BPI members".
While the BPI can identify which service providers have customers breaking filesharing rules, only the ISPs themselves can identify the exact customers.
It was unacceptable for ISPs to turn a "blind eye to industrial-scale copyright infringement", said BPI chairman Peter Jamieson.
"We are providing unequivocal evidence of copyright infringement via their services," he said.
"It is now up to them to put their house in order and pull the plug on these people."
C&W acknowledged it had an "acceptable use policy" for itself and its ISP, Bulldog, which covered illegal filesharing.
"This would normally mean that any accounts used for illegal filesharing are closed. We will take whatever steps are necessary to put the matter right," the firm said in a statement.
Meanwhile Tiscali said: "We do not automatically suspend customer accounts on request, but on occasion do so pending investigation. We are reviewing the information the BPI has provided and will respond appropriately."
BPI has taken legal action in 139 filesharing cases. The four that have gone to court have produced verdicts in BPI's favour, while 111 individuals have settled out of court.