Direct action
Simon Davis, from the watchdog Privacy International, said he would be asking the Information Commissioner to "conduct a full investigation" and hoped it would be "a test case of the Information Commissioner's new powers".
"You rarely find an aspect where almost every aspect of the Data Protection Act (DPA) has been breached, but this is one of them," said Mr Davies.
"It fits perfectly for the term 'egregious misuse' of personal data," he added.
A spokesperson for the Information Commissioners Office (ICO) told BBC News that it "takes all breaches of the DPA very seriously".
"Any organisation processing personal data must ensure that it is kept safe and secure.
"The ICO will be contacting ACS:Law to establish further facts of the case and to identify what action, if any, needs to be taken."
BSkyB is yet to make an official statement on the matter, but said it was investigating the breach.
The attack on ACS:Law is the latest in a number of high-profile attacks by piracy activists.
Last week, hackers temporarily knocked out the websites of the Motion Picture Association of America (MPAA) and the Recording Industry Association of America (RIAA).
The attacks were declared on notorious message-board 4chan and were reportedly in retaliation for anti-piracy efforts against file-sharing websites.
Users of 4chan are renowned for online activism and direct action. "Operation Payback", as it was known, was reportedly revenge for the MPAA and RIAA's action against The Pirate Bay.
The group has declared it will continue to target other sites involved in anti online piracy activity.
Social Networking Bookmarks