By Lauren Said-Moorhouse, CNN

(CNN) -- British lawmakers voted in favor of a key Brexit bill early Tuesday morning, marking an important milestone in the UK's exit from the European Union.

Members of Parliament passed the European Union (Withdrawal) Bill -- which will transfer EU law into UK legislation when Britain exits the bloc -- by 326 votes to 290.

The bill will now move onto committee stage and undergo line by line scrutiny.

Following the vote, Prime Minister Theresa May issued a statement calling it "a historic decision to back the will of the British people."

"Although there is more to do, this decision means we can move on with negotiations with solid foundations and we continue to encourage MPs from all parts of the UK to work together in support of this vital piece of legislation," she said.

Before the vote,David Davis, the UK's secretary of state for exiting the EU, emphasized that the bill offers businesses and individuals "reassurance that there will be no unexpected changes to our laws after exit day" while avoiding "a cliff edge of uncertainty."

He added: "The British people did not vote for confusion and neither should Parliament."

In addition to codifying existing EU laws, the legislation -- previously referred to as the Great Repeal Bill -- means the UK would no longer have to adhere to new laws made in Brussels after the country's departure from the bloc.

Amendments are expected to be added to the bill under pressure from backbench Conservatives and opposition members of Parliament when it moves into committee stage.

Opposition: Bill is a 'power grab'

May's government faces opposition over measures known as Henry VIII powers, which opponents say constitute a "power grab" and give ministers more power than Parliament. The government has said those powers will not be used for any significant changes but rather for technical amendments and only for a limited time.

Labour leader Jeremy Corbyn had instructed his party to vote against the legislation.

"Parliament has already voted to leave the European Union. But the government's EU Withdrawal Bill would allow Conservative ministers to set vital terms on a whim, including of Britain's exit payment, without democratic scrutiny," a Labour spokesperson told CNN on Monday.

Despite attempts from Labour, the Liberal Democrats and Scottish National Party to band together in opposition to the bill, the post-midnight vote was a comfortable victory for May.

This first Commons win is a welcome boost for the Prime Minister after Britain endured a difficult start to negotiations with Brussels, highlighted by last week's frosty encounter between Davis and his European counterpart, Michel Barnier.

Barnier complained of "no decisive progress" in the negotiations and accused Britain of attempting to secure the "impossible" in its approach to leaving the single market while retaining its benefits.

The-CNN-Wire™ & © 2017 Cable News Network, Inc., a Time Warner Company. All rights reserved.