LONDON — British leaders agreed on Monday to allow Parliament to debate, amend and vote on the terms of its exit from the European Union, in a concession to rebellious lawmakers who have demanded more power over the process.

The Brexit minister, David Davis, made the announcement just as Parliament was preparing for debates Tuesday over a bill on Britain’s withdrawal from the European Union, or Brexit. In eight scheduled debates, lawmakers will consider 186 pages of amendments, including some that would stop the government from concluding a deal without their express approval.

Mr. Davis’s announcement seemed intended to soften lawmakers’ resistance ahead of the debates and speed the passage of the withdrawal bill, which would transfer existing European law to the British statute books.

“Parliament will be given time to debate, scrutinize and vote on the final agreement we strike with the European Union,” he said. “This agreement will only hold if Parliament approves it.”

The concession underlines Prime Minister Theresa May’s weakness as she tries to allay the fears of big business and win support for the legislation. Within her own Conservative Party, as many as 40 lawmakers are prepared to support a no-confidence vote that would remove her from her post, The Sunday Times reported, just eight short of the number needed.

Meanwhile, in a letter leaked to the The Mail on Sunday, two cabinet secretaries, Michael Gove and Boris Johnson, have pressed Mrs. May to begin preparing to leave the European Union in the absence of any transition agreement. They urged her to set a firm date of June 30, 2021, for that to happen.

She also faces a frontal challenge from the Labor leader, Jeremy Corbyn, who has called her too weak to stand up to “no-deal extremists” within her own party.

“This is now crunchtime,” Keir Starmer, Labor’s Brexit spokesman told the BBC early on Monday. “I think it’s blindingly obvious to everyone who is following the negotiations that the final agreement with the E.U. is not going to have been agreed by March of 2019, and we need a bridge, or transitional arrangements.”

Mr. Starmer welcomed the news that Parliament would be allowed to vote on the agreement, and said the government must accept a range of further amendments that Labor lawmakers would propose on Tuesday, in an effort to protect British jobs. “This is a significant climb down from a weak government on the verge of defeat,” Mr. Starmer told lawmakers.

Labor lawmakers pointed out that the concession does not give Parliament power over a “no deal” scenario urged by right-wing Tories, in which Britain would leave the bloc with no transition agreement. “Parliament would be effectively sidelined, which makes a mockery of parliamentary sovereignty,” Chuka Umunna, a Labor lawmaker, said on Twiitter. “He calls it a meaningful vote — it is a fake one.”

Mrs. May also faced pressure on Monday from European business leaders, who urged her in a meeting at No. 10 Downing Street to avoid a “cliff edge” exit by agreeing to remain in the customs union and the single market.

Martin Wansleben, the head of Germany’s chambers of commerce, warned that the automotive industry would face more than $2.3 billion in additional tariffs annually if trade between the United Kingdom and the European Union fell under World Trade Organization regulations.

The concession marks the latest blow to Mrs. May, who became prime minister in June 2016, in the aftermath of the Brexit referendum. Her authority has corroded steadily in recent months. Last week saw the resignation of two of her cabinet ministers, and at least two more are under pressure to step down.