The curse on the crew of the Flying Dutchman damned them to sail the seas for eternity with no hope of ever reaching port. It came to mind during the dark tempests in which parliament first dismasted the government by rejecting its Brexit deal and then voted to leave that same government afloat. In the hope of gathering some intelligence about how the captain of the Brexit ghost ship intends to navigate her way out of this hell, I turned to a senior and clever Tory who is a close shipmate of the prime minister. How will it end? Came his sagacious reply: “I haven’t got a fucking clue.”

This much we do know. At 11pm on 29 March, one of three things must happen. Britain will crash out of the EU without a withdrawal agreement or a transition period. This will mean the overnight termination of decades of legal and trading agreements with both our continent and the rest of the world, an outcome that will deal severe reputational damage to this country and unleash disruption for which it is not at all prepared. Or Britain’s politicians will have to collectively confess that they cannot find a solution and seek to prolong or revoke the withdrawal process, damning us to sail on without landfall in sight unless this is accompanied by the promise of another referendum to resolve the deadlock. Or parliament will, very hard against the deadline, finally give its approval to something. This may not be a safe harbour, but the approval of a withdrawal agreement would be a port of sorts until the beginning of the next stage of the negotiations covering future relations.

Securing a deal to remove Britain from the EU in an orderly fashion has been the defining challenge of Mrs May’s premiership and parliament pronounced her an abject failure on Tuesday night. It took just minutes for MPs to vote down the agreement that she has been negotiating for nearly two years. Defeat by a margin of 230 votes is the largest loss on a non-trivial issue inflicted on a government in parliamentary history.

If the traditional laws of the political sea still applied, such an eviscerating rebuke would have led to the instant resignation of Mrs May as national captain. Yet though her compass is smashed, she remains lashed to her broken helm. Her party can’t dismiss her from duty because the failed coup by the ultra-Brexiters before Christmas made her safe from another attempt for a year. Labour can’t make her go, as was demonstrated by the predictable defeat of the no-confidence motion on Wednesday. The Tories and their ballast from Northern Ireland would prefer to sail this cursed sea rather than risk handing the ship of state to Jeremy Corbyn.

There were many ironies to savour on the night of Mrs May’s ignominy. Anna Soubry and the most ardent Tory Europhiles made temporary common cause with Jacob Rees-Mogg and his Brextremists. The Labour leader marched his party into the same No lobby as Boris Johnson, who rubbed shoulders there with Vince Cable and the Scottish Nationalists, each with very different and often completely contradictory motives for killing Mrs May’s deal. When news reached the crowds in Parliament Square, the humiliation of the prime minister was cheered both by the gang from Leave Means Leave and by the throng who had come to clamour for a people’s vote. Both those who want to reverse Brexit and those who yearn for the starkest of Brexits think that Mrs May’s defeat paves the way to ultimate victory for their cause. Both cannot be correct. One or other will eventually look back at that night as a terrible mistake.

‘Jeremy Corbyn, a man whose career and image is all about disdaining flexibility and compromise.’ Photograph: Will Oliver/EPA

This has provided the one straw of consolation that Mrs May is now clinging to. Her defeat tells us what parliament does not want, but leaves us no better informed about what, if anything, MPs will approve. There is no majority for her deal; there is also no proved majority for any of the alternatives.

This leaves the prime minister, weakened as she is, with some continuing control of the process. One possible way forward is for her to cut her losses with the ultras on her side and try to find a majority in parliament by reaching across the aisle to MPs from opposition parties. This would require a dramatic tack to a softer version of Brexit and the erasure of some of her red lines. There is a Remainer wing of the cabinet who favour that approach; they have always tried to push their leader in the direction of a less abrupt Brexit. Mrs May has been trying to keep them happy and present herself as a reasonable woman by inviting opposition MPs in for talks, but I don’t think she is pursuing this avenue with any conviction. To broker a compromise that would attract support from other parties, she would have to display high levels of creativity and suppleness when these qualities have been entirely absent from her character. It is not exactly likely that a prime minister who has trumpeted obduracy as a virtue can suddenly become the emollient consensus-seeker. Even if she could change into a different person, it is desperately late. Too much poison has flowed, divisions have become too entrenched, too many of the other actors have painted themselves into irreconcilable positions.

There are versions of a softer Brexit, such as embracing permanent membership of a customs union, which might attract some support from opposition MPs, but the numbers willing to do so would be lower than might once have been the case. Remainer MPs who could have embraced that sort of compromise a year ago will no longer do so, because they now think they have a chance of reversing Brexit altogether. At the same time, the inflammation of the passions on her own side has escalated the chances of the Tory party reacting to a softer Brexit by imploding. Another slew of resignations from the cabinet would be the least of it. “The Conservative party might well split in half,” says one senior minister.

To consider the destruction of her party and her government a risk worth taking, Mrs May would have to be really confident that Labour would deliver enough of its MPs to get a new Brexit deal through parliament. That would require a prime minister who trusts virtually no one in her own party to place her trust in Jeremy Corbyn, a man whose career and image are all about disdaining flexibility and compromise. The two of them cannot even agree on the terms of talks just as they previously could not even agree on a format for a TV debate. The working assumption in Number 10 is this: even if Mrs May were prepared to shift towards a softer withdrawal, the Labour leader will always find a fresh reason to reject whatever she comes up with because he wants this to be branded as a “Tory Brexit”. It is hard to argue that this reading of Mr Corbyn is wrong.

Absent Mrs May being capable of reaching a cross-party agreement, her plan B is to revert to plan A. Incredible as this might seem in the wake of such a crushing defeat, the prime minister thinks her least worst option is to try to breathe life back into the deal that parliament has pronounced dead. I am told by someone very familiar with her thinking that bringing back a tweaked version of her deal is the prime minister’s preferred plan of action “by a mile”. To be successful, this would require 117 MPs to change their minds.

Achieving that relies on two heroically optimistic assumptions. One is that the EU will make sufficient concessions, especially around the Northern Ireland backstop, to meet the demands of the Brexit fundamentalists. The second assumption is that these people will ever be content. Even if the EU were to say yes to what they currently say they want, on past form, the insatiable ultras are not people who can be trusted to take yes for an answer.

Some MPs are working to effectively relieve the prime minister of command by taking control of the process away from her and handing it to parliament as a collective. Others would then get the responsibility for trying to locate a solution capable of assembling majority support – and then finding someone to go and try to negotiate it with the EU.

If there is no majority for anything, then the choices become stark. Britain will career out of the EU with no deal or Brexit will have to be postponed pending another referendum to ask the people to deliver a verdict on this ocean of tears. The phantom ship and its spectral crew sail deeper into uncharted waters.

• Andrew Rawnsley is an Observer columnist