London (CNN) British Prime Minister Theresa May has told Conservatives lawmakers she will not fight the next general election in 2022, a member of parliament attending the meeting told CNN.

The pledge came as May was making her final pitch to Conservative Members of Parliament on Wednesday evening before they started voting in a secret ballot which began at 6 p.m. (1 p.m. ET).

The Prime Minister "got a real grilling, but overall solid support" as she made her case to Conservative lawmakers, a separate pro-May MP told CNN.

Theresa May addresses the media outside 10 Downing Street after it was announced that the Conservative Party will hold a vote of no confidence in her leadership.

May vowed to fight for her political life Wednesday morning after a vote of no-confidence in her leadership was called by members of her own party over her handling of Brexit. If she loses the vote, she will be out as Conservative leader.

The starting gun was fired after 48 Conservative MPs submitted letters demanding a vote to the 1922 Committee, which represents rank-and-file Conservative lawmakers in the House of Commons.

Appearing on the steps of Downing Street, May was in bullish mood, promising to fight the contest with "everything I've got."

Graham Brady, the MP who chairs the committee, confirmed that the threshold for a confidence vote -- equivalent to 15% of Conservative MPs -- had been passed.

In a statement, Brady confirmed that the result of the vote would be made as soon as possible with ballots being counted immediately.

Graham Brady, chairman of the Conservative Party 1922 Committee of MPs, speaks to the media outside the Houses of Parliament on December 12.

He told CNN that if May was to lose the vote, a replacement could be found quickly.

"I ran the process in 2016," Brady said. "It took no more than 10 days -- it might even be possible to conduct a process of that sort more quickly.

"If there are two candidates, and that is the expectation -- there will be a postal ballot and that inevitably takes longer."

He also explained the announcement was made early Wednesday to avoid unsettling the markets.

"We thought that when we were making a serious announcement that has important consequences, we thought that we ought to make the announcement before the markets open," he added.

The vote could hardly have come at a worse time for May, who has been criss-crossing Europe to beg EU leaders for help passing her Brexit deal through the UK Parliament.

May was forced to postpone a vote on the deal on Monday when it became clear she was likely to go down to a humiliating defeat.

If May loses the no-confidence vote, the Conservative Party must hold a leadership election. If she wins, however, party rules mean that she cannot face another vote in a year.

May is facing considerable pressure from the Euroskeptic wing of the party. In a statement published on Wednesday, Jacob Rees Mogg, chairman of the European Research Group and Steve Baker, his deputy, urged her to go.

The Country needs a new leader, it is time for Mrs May to resign. — Jacob Rees-Mogg (@Jacob_Rees_Mogg) December 12, 2018

"Theresa May's plan would bring down the Government if carried forward. But our party will rightly not tolerate it," read the statement carried by the UK Press Association.

"Conservatives must now answer whether they wish to draw ever closer to an election under Mrs. May's leadership. In the national interest, she must go."

May later faced a fiery House of Commons during Prime Minister's Questions, trading blows with opposition leader Jeremy Corbyn.

Speaker John Bercow was forced to call for calm on several occasions as Corbyn pressed May on her reasons for postponing the Commons vote on her Brexit deal, calling her behavior "appalling."

"Her behavior today is just contemptuous of this parliament and of this process," said Corbyn.

"The Prime Minister's appalling behavior needs to be held to account by this House as indeed the people of this country are more and more concerned about the ongoing chaos at the center of her government."

"The time for dithering and delay is over," he said.

Ian Blackford, the Scottish National Party's leader in Westminster, called the Prime Minister a "disgrace" for delaying the vote.

"Prime Minister -- take responsibility, do the right thing, resign," said Blackford.

Support for May

Former Prime Minister David Cameron, who called for the referendum on the UK's membership of the European Union before resigning immediately after the result, urged the party to back May in the leadership vote.

I hope Conservative MPs will back the PM in the vote today. We need no distractions from seeking the best outcome with our neighbours, friends and partners in the EU. — David Cameron (@David_Cameron) December 12, 2018

"I hope Conservative MPs will back the PM in the vote today. We need no distractions from seeking the best outcome with our neighbors, friends and partners in the EU," he tweeted.

A number of government ministers came out in support of May just minutes after the vote of no confidence was announced.

The PM has my full support. At this critical time we need to support and work with the PM to deliver on leaving the EU, & our domestic agenda - ambitious for improvements to people's lives & to build on growth of wages & jobs. — Amber Rudd MP (@AmberRuddHR) December 12, 2018

"The PM has my full support. At this critical time we need to support and work with the PM to deliver on leaving the EU, & our domestic agenda -- ambitious for improvements to people's lives & to build on growth of wages & jobs," tweeted Amber Rudd, the Work and Pensions Secretary.

Chancellor Philip Hammond also defended May , tweeting that she had "worked hard in the National interest since the day she took office and will have my full support in the vote tonight."