BT and TalkTalk are asking the Court of Appeal to reconsider their concerns with the Digital Economy Act, after the High Court ruled in April that the legislation is legal.
The two firms' initial challenge failed when the judge agreed only to their concerns that ISPs should not have to pay any of the cost of setting up a system of monitoring and enforcement of alleged copyright infringers.
In other respects, judge Kenneth Parker argued that the Digital Economy Act is a credible system for combating copyright infringement.
"From the point of view of copyright owner and subscriber, the Digital Economy Act represents a more efficient, focused and fair system than the current arrangements," he said in his ruling at time.
However, BT and TalkTalk continue to argue that the measures in the legislation that aim to prevent online copyright infringement are inconsistent with European law and could harm the basic rights and freedoms of consumers.
Many MPs, consumer groups and other communications providers agree with this contention, arguing that the Act received insufficient scrutiny before it was rushed through parliament in the wash-up process.
The Department for Media, Culture and Sport (DCMS) said in a statement it was aware of the firm's appeal but was confident the Act would remain in place.
"We note BT and TalkTalk's decision to apply to the Court of Appeal against the judicial review ruling," it said.
"The government remains confident that the ruling delivered by the High Court was the correct one, and is continuing work to implement the Act accordingly."
It is unlikely the challenge will have any impact in the near future as it can take up to three months for the court to decide if the firms have the right to appeal and another two to nine months for a hearing date to be set.
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