It’s now all or nothing. Theresa May has gone, most likely taking with her the possibility of a negotiated exit from the European Union. It means that the choice that will soon face the country is starker than before: a no-deal Brexit – or no Brexit at all.

In her parting address outside Downing Street, May made a better case for compromise between those two positions than she ever had before. “Life depends on compromise,” she said, quoting the Kindertransport rescuer and hero, Nicholas Winton. It sounded hollow coming from her, given that her brittle personal style, incapable of emollience, and her inept grasp of political tactics had together made her a byword for inflexibility (right until the moment, which came often, when she would cave entirely). Her epitaph will be the inadvertent slogan of her calamitous 2017 election campaign: “Nothing has changed.”

Given what is likely to follow, we might look back wistfully at a PM who at least sought to smooth our departure

And yet all that concealed the fact that May’s eventual Brexit strategy – arrived at only after she had legitimised, with fateful consequences, the notion that “no deal was better than a bad deal” – was the pursuit of a compromise between no deal and no Brexit, in the form of a withdrawal agreement.

The result is that those who fear the chaos that would be unleashed by a no-deal crash out of the EU might come to feel an unexpected nostalgia for May and her hapless but dogged efforts. Given what, and who, are likely to follow, we might look back wistfully at a prime minister who at least sought to smooth our departure from the bloc of our closest trading partners and neighbours. To picture Boris Johnson in No 10 is to realise: we may miss her when she’s gone.

For the prospect now is that May’s abject failure to pass her withdrawal deal has discredited the very idea of such an agreement. That effect is due to be cemented when the results of the European elections are tallied this weekend. Even if Nigel Farage’s Brexit party doesn’t match its sky-high expectations – and turnout figures do look healthier in remain areas – Farage’s expected trouncing of the Tories among leave voters has already persuaded, or panicked, plenty of Conservative MPs towards the view that the only Brexit that will fly electorally is one of the “clean break” variety. Hence the stampede to Johnson, in the hope that he can match Farage in championing a populist, pure brand of Brexit.

Play Video 2:01 As Theresa May resigns, how will she be remembered? – video

Which is not to say that Johnson, or any other leader, might not try to succeed where May failed, by attempting to negotiate a new agreement with Brussels that will somehow command a majority in the House of Commons. But such a quest implies that a better deal was – and still is – there to be had from the EU, if only May had been a better poker player. Those who know the EU well insist that’s a delusion, that not only will the EU27 not reopen the treaty they agreed with a departing UK – a stance reiterated by an EU spokesman today – but they cannot reopen it. They’ll insist the agreement represents the only possible arrangement consistent with the red lines May painted from the start. It’s a matter of fundamental political geometry; there is no other shape available. Unless a new prime minister were to give way on, say, free movement, or the UK’s ability to make its own trade deals, May’s deal is all there is. It’s the last word.

That, surely, is especially true of Johnson. “He’s the last person to get anything out of Brussels,” one minister tells me, reflecting on the former foreign secretary’s standing in European capitals. There is a rare consensus among the continent’s leaders on this point: they regard Johnson as a loathsome charlatan, a Trumpian peddler of EU myths with a record of mendacity that stretches back to his 1990s spell as a Telegraph correspondent. Even if they could bend on, for instance, the Northern Ireland backstop, the EU27 would be deeply reluctant to do so, knowing they’d be turning Johnson into a hero.

So the question is, how will May’s successor respond to the stubborn fact that there is no better deal, that there are no “alternative arrangements”? Some Tory remainers hope for an outbreak of honesty, as the new prime minister tells their party that the Brexit of their dreams cannot, after all, be done. This is what explains the modest, remainers-for-Boris grouping typified by the columnist Matthew Parris, most of them relying on the Nixon-to-China precedent. If it took a seasoned anti-communist like US president Richard Nixon to sit down with Chairman Mao, then perhaps it will take an arch-leaver like Johnson to break Brexiter hearts and tell them the dream is over.

EU leaders stick to Brexit guns as they prepare for 'different breed' of PM Read more

That could take the form of re-offering May’s thrice-rejected deal. But, given the arithmetic of the Commons and the impossibility of crafting a Brexit acceptable even to all Brexiters, that hardly looks promising. You can see why May’s successor might instead be tempted by the no-deal option. It would shut Farage up; and it would delight the noisy, troublesome faction that has made life hell for successive Tory leaders for four decades, with May only the latest to be devoured. What’s more, a research paper from the Institute of Government is doing the rounds, arguing that MPs no longer have any clear mechanism to stop a no-deal exit; the devices they had before have fallen away. If a prime minister wants to crash out, perhaps by simply running out the clock and waiting for the EU extension to expire on 31 October, it would be a “near-impossible task” for MPs to stop them. And that’s especially true if the resolve of some Tory MPs, previously hostile to no deal, weakens, thanks to fear of Farage and the dynamic of a new leader. One remainer minister fears that such an erosion of opposition to no deal is “perfectly logical and plausible”.

The battlefield is shifting, towards a starker, binary clash of no deal versus remain. That means pro-Europeans will have their work cut out. First, they will need to argue that these latest changes in the landscape in no way represent a mandate for a no-deal Brexit. Farage might top the Euro election poll, but winning one-third of the vote on, say, a one-third turnout is not a national mandate. That will be truer still of a new prime minister installed on the votes of 300-odd MPs and the tiny, ageing sect that is the Conservative party membership, a group wholly unrepresentative of the nation as a whole. A no-deal Brexiter may well win the Tory contest; it does not mean they will have a mandate to crash this country into economic and diplomatic disaster.

Play Video 1:51 David Cameron says he feels 'desperately sorry' for Theresa May – video

Opponents of the nightmare scenario must not succumb to defeatism. Sure, the procedural task in the Commons might be more complicated now. But that does not make it impossible. If there’s the political will in the chamber and the country to prevent no deal, there will be a procedural way. Tory remainers will still hold a powerful weapon: they can threaten, as Dominic Grieve did on Thursday, to join the opposition parties in backing a no-confidence vote and bringing down the government, if that’s what it takes to stop a Brexit catastrophe.

This is the argument to press: that there is no mandate for a no-deal Brexit, a scenario that was not even countenanced, let alone approved, in the 2016 referendum. If a new Tory prime minister wants to exit that way, he or she will need fresh public consent. That could be a new public vote or a general election, although it’s hard to imagine the Tory leader eager to face the country with Brexit still undone. Which is why campaigners for a second referendum believe that all roads still lead back to them: even Brexiters, they say, will eventually conclude that a public vote is the only way to break the impasse.

Perhaps this will be the endgame, a referendum offering two final options: no deal or no Brexit. With no withdrawal deal to approve or reject, there will be no other question to ask. Both remainers and hardcore Brexiters should feel their palms grow clammy at that prospect. By holding out and refusing to back May’s deal, they may well have seen off the possibility of a phased exit. The result will be that we either stay in the EU – or crash out altogether. May has gone, and suddenly the stakes have got much higher.

• Jonathan Freedland is a Guardian columnist