MPs backed the EU Withdrawal Bill by 326 votes to 290 despite some critics branding it a "power grab" by ministers.
British Prime Minister Theresa May overcame a major Brexit hurdle as her bill to transfer the body of European Union law onto the United Kingdom statute books progressed with the support of a majority of MPs.
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Arch-Brexiteer Peter Bone said: "I would be very surprised if this bill finishes up in exactly he same format at the end... it seems to me the government will be well advised to accept the reasonable amendments that improve the situation".
It meant "we can move on with negotiations with solid foundations", she said.
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The bill is aimed at repealing the 1972 law through which Britain joined the bloc, transferring in bulk around 12,000 existing European Union regulations onto the British statute books.
The bill will now pass to the committee stage where MPs will have more opportunity to put forward amendments, before the bill goes to a vote in the House of Commons again.
"We have had two days of informed and vibrant debate and as the Bill proceeds through Parliament we will look with the utmost seriousness at the amendments that are tabled".
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However, about a dozen Labour MPs from Leave-backing constituencies could rebel against Jeremy Corbyn's orders.
The bill proposes the broad use of existing "Henry VIII powers" that allow ministers to amend legislation without full parliamentary scrutiny.
The Welsh Government has confirmed it will formally object to Theresa May's plan to transfer European Union laws to the United Kingdom at the point of Brexit.
Some want assurances that the government will not misuse its power, others want to make sure the protections of certain workers rights are also written into the bill before allowing it to move to the unelected upper house of parliament.
The SNP's 35 MPs voted against, with worldwide affairs spokesman Stephen Gethins describing the legislation as a "dark day for devolution and democracy".
Speaking to Sky News, shadow Brexit minister Jenny Chapman said: "Labour will not block Brexit".
Opening the debate, Brexit secretary David Davis told MPs that the bill would ensure that the United Kingdom would leave the EU "safe in the knowledge that we are ready for day one of exit", adding that "a vote against this bill is a vote for a chaotic exit from the European Union". "But the flaws are so fundamental it's hard to see how this Bill could ever be made fit for purpose".
May had accepted an invitation from the parliament to speak at a meeting of the heads of party groupings, he said.
To the frustration of some of her colleagues, Flint said she accepted the bill's scope of powers would need attention but said it was not Labour's job to kill it.
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