British Prime Minister Theresa May staked everything on getting her Brexit deal, and its rejection on Tuesday has left her authority severely damaged.

The Conservative leader had already sparked anger and frustration at home and in Brussels for taking the Brexit talks down to the wire.

These have now been shown to have failed, with dozens of her own MPs voting for a second time to reject her EU withdrawal agreement.

"The PM has lost all control. If she had an ounce of decency she'd resign," said opposition Labour lawmaker Lou Haigh.

After her defeat, May continued to insist that her deal was the best option, but said she would - as promised - allow MPs now to vote on whether to leave the EU with no deal.

But faced with the prospect of another rebellion, she said Conservative MPs can vote as they choose - a move that commentators said showed how little authority she had over her party.

"For a government not to be able to whip its MPs on one of its absolutely central policies is not exactly … normal," noted Alice Lilly, senior researcher at the Institute for Government.

May has made much of her reputation for toughness, gleefully adopting a colleague's description of her as a "bloody difficult woman".

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But her efforts to seek changes to her own divorce deal just weeks before exit day on March 29, and despite EU warnings that her demands were impossible, have tested MPs' patience.

Pro-European ministers staged a revolt, demanding May offer a vote on delaying Brexit rather than allow Britain to leave with no deal at all.

Meanwhile many Eurosceptics are livid at her failure to deliver the decisive divorce she had promised.

"This is a total failure of leadership," said leading Brexit campaigner Nigel Farage after Tuesday's vote.

May took office after the 2016 referendum, and despite having campaigned to stay in the EU, embraced the cause with the mantra "Brexit means Brexit".

Her promise to leave the EU's institutions and end free movement of workers delighted Eurosceptic MPs, but caused dismay among many pro-Europeans.

The splits in her Conservative party became a serious problem after a snap election in June 2017, when May lost her parliamentary majority.

She was forced to strike a deal with Northern Ireland's pro-Brexit Democratic Unionist Party (DUP), and since then has struggled to keep her party and its allies together.

"At first she appeared to be a unifier, but she turned out to have too little courage, imagination or skill to lead the Brexit negotiations," said the Conservative-backing Spectator magazine.

Naturally reserved and reliant on her husband Philip and a few close aides, May often says she is just quietly "getting on with the job".

But in the last election, she struggled to engage with voters and was dubbed the "Maybot" after churning out the same answers and speeches over and over again.

Critics complain of similar difficulties in communicating during the Brexit talks.

Matthew Parris, an anti-Brexit former Conservative MP who now writes for The Times, described her as "the living embodiment of the closed door".

But May has been written off before.

She survived the resignations of a string of high-profile Brexit supporters, notably former foreign secretary Boris Johnson.

May also won a confidence vote in her Conservative party over Brexit in December, making her immune from a similar challenge within a year.

She was forced to promise to quit before the next scheduled election in 2022, however, and even then, one third of her MPs voted to unseat her.

May's office indicated she had no intention of resigning after Tuesday's vote.

James Cleverly, deputy chairman of her Conservative party, said she was driven by her commitment to delivering Brexit.

"The prime minister is having to navigate a very, very difficult course through the unique set of circumstances we are being presented with," he told the BBC.