Pat McFadden says the so called Great Repeal Bill, which will formally enact Brexit, contradicts the wishes of Leave voters to depart from EU laws.
He branded the bill 'a giant power grab' from ministers, while fellow Labour MP Emma Reynolds said it left 'big question marks' over Britain's future relationships with EU regulatory agencies.
The bill ensures the same laws apply in the UK after departure from the EU in March 2019, when the UK Parliament will have the power to change them.
Brexit Secretary David Davis said he will 'work with anyone' to make it a success, but Labour has said it will not support the bill in its current form.
Shadow Brexit secretary Sir Keir Starmer has demanded concessions in six areas, including the incorporation of the European Charter of Fundamental Rights into British law.
Wolverhampton South East MP Mr McFadden, who sits on the influential Brexit Select Committee, said: “There’s a paradox at the heart of this bill.
"It incorporates all existing EU law into UK law in order to give certainty to the public and to businesses going forward yet the purpose of leaving the EU is to depart from those same laws.
"So even if there is certainty on day one, it might not last for very long.
"From Labour’s point of view we will want to preserve in particular the employment and social rights that are currently guaranteed by EU law and we will also oppose the idea of ministers getting too much power to change laws in the future without proper debate by Parliament.
"We were told that coming out of the EU would mean more powers for our own Parliament but the way this is being done it looks like a giant power grab from ministers rather than a bill to increase the powers of our own Parliament.”
Ms Reynolds, the Wolverhampton North East MP, who is also a member of the committee, said: "I hope the Government honour their promise that there will be no dilution of employment laws and regulations for consumers and the environment.
"Big question marks remain over our future relationships with EU regulatory agencies, such as the European Aviation Safety Agency.
"It will be a huge task if we bring in domestic agencies to do the equivalent work."
Scotland’s first minister Nicola Sturgeon and Carwyn Jones, the Welsh first minister, have said that their governments will not give the bill legislative consent unless there are major changes to it.
Lib Dem leader Tim Farron said the passage of the bill could be 'a political nightmare that could end Theresa May’s premiership'.
The Conservatives are relying on support from the DUP to get the bill through after losing their Commons majority in the General Election.