The legislation, which became law earlier this year, is supposed to bring transparency to the lobbying of ministers and senior civil servants.
However it has been widely denounced by charities and campaign groups, who say it will restrict their campaigning during elections, while critics say the measures on professional lobbyists are so weak they amount to a "lobbyists charter".
The shadow leader of the Commons, Angela Eagle, said that a Labour government would replace it with a universal register of all professional lobbyists backed by a code of conduct and sanctions.
"The Tory-led Government's gagging law is an illiberal attack on our democracy," she said.
"It was cooked up in a shabby deal between David Cameron and Nick Clegg. It lets vested interests off the hook, and it gags charities and grassroots campaigners who want to hold the Government to account for their broken promises at the next election.
"Labour will repeal the Act and will instead legislate for the reform that our politics needs. We will do what Cameron and Clegg didn't - and consult with charities and campaigners about how to ensure transparency in our elections while protecting freedom of speech."
The legislation finally received the Royal Assent in February after a turbulent passage through Parliament, with ministers forced to use their Commons majority to overturn a series of amendments by the House of Lords.