The Act, which covers a number of issues including measures designed to tackle internet piracy, became law in April this year.
However, both ISPs told the BBC the Bill was "rushed through" and had "insufficient scrutiny". The two firms are also concerned that measures to tackle net piracy - including plans to temporarily suspend people from the web - could be in breach of "basic rights and freedoms".
In May, Ofcom, which had been charged with overseeing how the measures would be implemented, issued a draft Code of Practice that said ISPs will have to send warning letters to web users suspected of illegal file-sharing. The details of those that have received three or more notifications in a year can be request by copyright holders in a bid to start legal action.
However, the code will initially only apply to fixed-line ISPs with over 400,000 subscribers, meaning the UK's seven largest internet access providers; BT, TalkTalk, Virgin Media, Sky, Orange, O2 and the Post Office, will be required to conform to the code.
"It means we could have huge swathes of customers moving to smaller ISPs to avoid detection," said Andrew Heaney, executive director of TalkTalk.
BT and TalkTalk also want a High Court to clarify whether the Code of Practice conflicts with the EU's e-commerce directive that says ISPs are "mere conduits" of content and should not be responsible for the activities customers use their networks for.
"It's disappointing that we feel the need to take action but we feel we have no choice. We have to do this for our customers who otherwise run the risk of being treated unfairly," said Gavin Patterson, CEO of BT Retail.
"Our dispute is not with the current Government but with the previous administration which pushed this through without due process. We need clarity about whether this legislation is compatible with important EU laws."
Charles Dunstone, chairman of the TalkTalk Group, said innocent broadband customers will suffer and citizens will have their privacy invaded.
"We think the previous Government's rushed approach resulted in flawed legislation. That's why we need a judicial review by the High Court as quickly as possible before lots of money is spent on implementation."
Any laws passed before a general election can be repealed by a newly elected government. However, the current coalition government has already said it has no plans to repeal the Act.
"The Digital Economy Act sets out to protect our creative economy from the continued threat of online copyright infringement, which industry estimates costs the creative industries, including creators, £400m per year," the Department of Business, Innovation and Skills told the BBC
"We believe measures are consistent with EU legislation and that there are enough safeguards in place to protect the rights of consumers and ISPs and will continue to work on implementing them."