Internet service providers (ISPs) BT and TalkTalk are refusing to give up their fight to have the Digital Economy Act removed from the statute books.
The broadband providers, whose joint judicial review of the controversial anti-filesharing legislation was turned down last month, have announced plans to appeal the decision.
Under the act - passed in April 2010 in the final days of the Labour government - individuals suspected of internet copyright infringement face disconnection by their ISP.
However, critics of the legislation argue that this places an unfair burden on broadband providers to monitor and police the activities of their subscribers.
BT and TalkTalk also claimed that the legislation – enacted during last year's parliamentary wash-up period – was given inadequate scrutiny in the House of Commons.
However, the High Court sided with the government on the Digital Economy Act, ruling that the legislation was broadly compatible with EU law.
The only concession made to the broadband industry was the removal of a clause instructing ISPs to contribute to the costs incurred by Ofcom in administering the regime.
In a written statement, BT claimed that the High Court's conclusions on "many of the other important and complex issues put before it" were "not robust enough" to provide the certainty and clarity sought by the claimants.
"This is why they are seeking leave to take the matter before the Court of Appeal," the ISP added.
"BT and TalkTalk have chosen to seek an appeal on four of the five grounds addressed in the initial High Court case."
These related to the EU's Technical Standards Directive, the Authorisation Directive, the E-Commerce Directive and the Privacy and Electronic Communications Directive.