BRUSSELS -- British lawmakers upended Prime Minister Theresa May's Brexit plans Wednesday by giving Parliament the final say on any exit agreement the government reaches with the European Union.

The House of Commons voted 309-305 to insert Parliament in the already strained Brexit process, dealing a blow to May's already fragile authority.

Labour Party Leader Jeremy Corbyn called the defeat "a humiliating loss of authority" for May, BBC News reports.

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Several lawmakers from the prime minister's governing Conservative Party sided with the opposition to insist that any withdrawal deal with the EU requires an Act of Parliament to take effect -- essentially giving lawmakers a veto on Brexit.

May had promised lawmakers a "meaningful vote" on the departure agreement, but political opponents said her assurance was not enough of a guarantee.

This vote was the government's first defeat in Parliament on its Brexit legislation.

It came as an amendment to the EU Withdrawal Bill, the government's flagship piece of Brexit legislation. The bill itself, which still is moving through Parliament, would convert some 12,000 EU laws into British statute on the day the U.K. leaves the bloc in March 2019. Without it, Britain could face a legal black hole the day after Brexit.

If the amendment survives a final vote on the withdrawal bill, it would not have a direct impact on Britain's negotiations with the EU. However, it could reinforce perceptions in the bloc that May lacks authority.

Earlier Wednesday, European Union chief Brexit negotiator Michel Barnier said there will be "no turning back" for Britain on commitments made during an initial divorce deal between the two, after his U.K. counterpart insisted it was merely a "statement of intent."

Barnier told legislators at the European Parliament that the negotiations so far have been "extremely complex and extraordinary" but insisted that he had made no concessions to the British side.

U.K. negotiator David Davis suggested over the weekend that the deal was less than cast in stone. The initial deal involved the maintenance of a transparent border between EU member Ireland and the U.K.'s Northern Ireland, as well as citizens' rights.

But Barnier said "progress has been noted and recorded and is going to have to be translated into a legally binding withdrawal agreement."

The European Parliament's chief Brexit official, Guy Verhofstadt, said Davis was already backtracking after his statement Sunday, which riled officials in Brussels.

Verhofstadt said he and Davis had spoken on Tuesday and that Davis "assured me it is absolutely not his intention, not the intention of the U.K. government, to backtrack on their commitments.

"The best way to secure this is that in the coming weeks we transpose all these commitments into the legal text of a withdrawal agreement," he said.

Most of the legislature had warm words for Barniers' performance in running a tight ship during the talks and keeping the 27 other EU nations united in their stance.

EU leaders open a two-day summit on Thursday during which they are slated to agree that there has been "sufficient progress" for the talks to move to the second phase of future relations and trade, a subject Britain wants to open as soon as possible.

Britain is due to leave the bloc in March 2019, but a Brexit deal will have to be agreed by the fall of 2018 to give national parliaments time to approve it.

European Union Council President Donald Tusk warned Tuesday that it would be a "furious race against time" to finish Brexit negotiations by autumn, saying only "moderate progress" has been achieved so far.