The iceberg is approaching and now the scramble for the lifeboats begins. The iceberg in question is the catastrophe of a no-deal crashout from the European Union, its contours and texture becoming ever sharper as 29 March gets closer. For now, most MPs are vehement in their insistence that they dislike the iceberg very much, and that they are passionately opposed to sailing right into it. But the law is clear: Britain leaves the EU on that date unless another law is passed to change course. In other words, standing on the deck shouting at the berg will not help. MPs have to agree a plan to get out of the way – and they have to do it very soon.

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Here’s how fast things are moving. On Tuesday night, Theresa May will watch as her deal sinks in the Commons. It might not take the battering predicted by BBC News, which projects a defeat by more than 220 votes. Indeed, it might end up being much narrower. That’s thanks to an amendment tabled by Labour’s Hilary Benn, which will give MPs the chance simultaneously to reject both May’s deal and a no-deal. Jacob Rees-Mogg’s crowd won’t want to do that – they think a collision with the iceberg will be bracing, shake things up a bit – so May might suffer a milder humiliation than was otherwise looming.

Then, thanks to Messrs Grieve and Bercow – not a Dickensian law firm but the double act of Tory rebel and troublesome Speaker – the government will have to return to the Commons within three working days to present its new plan. Chances are, it will be virtually the same as the old plan. The prime minister will tell MPs, once again, that if they want to avoid disaster, their only guarantee of safe passage is via her deal.

That’s when the scramble starts in earnest, with different camps offering rival lifeboats. Thanks to all that procedural activity in Westminster, MPs have won the right to offer alternatives to the May deal and to do so rapidly. One of these options is labelled Norway plus, the other a second referendum. MPs will have to choose which one offers the best shot at safety – because if both go down, we crash.

This choice will not be made calmly and deliberatively, with adequate time for reflection and debate. It’s more likely to be rushed and frantic. The minute one amendment is voted on and rejected, the next one will be up. So supporters of Norway – who seek a soft Brexit through which Britain would join the European free trade area (Efta), thereby staying in the single market, with customs union membership as the “plus” – could see their first choice rejected, only to have to make a decision immediately on whether to back a second referendum.

Much will depend on the sequence. Campaigners for a so-called people’s vote say their strategy has always been “to remove everything else from the table”, to ensure that a referendum is the last option left standing. They believe this week’s Commons manoeuvres demonstrated MPs’ rejection of no deal. Tuesday will eliminate the May deal. If Jeremy Corbyn tries and fails to pass a motion of no confidence in the government, the option of a general election falls away. Once Norway falls then, hey presto, there’s only one way to swerve away from the berg: another public vote. But what if the Speaker doesn’t play along, choosing instead for MPs to vote on a referendum first, before Norway has been rejected?

It means that all those who want to avoid the cataclysm of crashing out of the EU need to do their hard thinking now. Pro-Europeans especially need to guard against so dividing their forces between Norway and a referendum that neither option gains the critical mass it would need – in Westminster and the country – to prevail. The risk is that in dithering over which lifeboat is best, they run out of time and crash to disaster.

So how to weigh up this choice? The Norway plan has attracted renewed interest in recent days. On the Tory benches, the thoughtful Conservative George Freeman announced he’d back May and then, when that plan failed, support Efta membership. Meanwhile, the shadow chancellor, John McDonnell, is said to have had friendly conversations with the Norway group, and there have been other public smoke signals in that direction.

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McDonnell’s move suggests a shift in the Labour leadership’s thinking. The realisation has come that allowing a hard, or even no-deal, Brexit won’t just be blamed on the Tories: Labour too will be held responsible, including by its own devotedly pro-remain members. Accordingly, any earlier attraction to no deal as a route to economic collapse and calamity, after which the British public would thirst for a radical Labour government, has faded. On the other hand, the high command of the party does not much like the prospect of a second referendum – partly because they fear it would alienate leave voters, and partly because they regard the People’s Vote campaign warily, imagining it as a Blairite shadow army.

And yet it’s not easy for them to jump into the Norway lifeboat, either. True, Britain would stay in the single market, which avoids the economic self-harm of Brexit. But we would have lost our seat at the EU table, deprived of a voice and a veto. The bogus sovereignty arguments deployed by the Brexiteers would gain a validity they previously lacked.

If advocates of Norway are honest about what their model entails, it might prove a hard sell, especially to those who voted leave. As well as depriving the UK of a say in EU decisions, it will involve hefty cash payments and an ongoing commitment to free movement of people. And there’s no guarantee our European neighbours would even allow a country of Britain’s size to join Efta. Besides, people’s vote campaigners suspect some Tories are attempting to use the appeal of Norway to get Brexit across the line, only to harden our exit from the EU once we’ve formally left on 29 March. As one puts it: “You think you’re going for a nice weekend trip to Oslo, only to wake up in the frozen tundra of Canada.”

One remain MP is upfront, admitting he might well resort to Norway eventually, but not yet. Only when remain is certifiably dead as an option, if we leave on 29 March, will he countenance it. While there’s still a chance to stay in the EU, he’ll fight any form of Brexit, including even the softest, Norway version.

Which leaves only one lifeboat: a public vote. The case for a second referendum suffered a blow this week, at least among the 1.3 million who watched James Graham’s Brexit drama on Channel 4. It was a reminder of just how dispiriting and sour an affair the 2016 campaign was. No one could watch that and want to relive the experience. And because Britain still lacks any equivalent to the US’s Mueller investigation, we haven’t got to the bottom of either the methods or funding of the leave campaign – including its use of social media, the focus of the Channel 4 film. We can hardly be confident that the same tricks won’t be used again.

And yet, what other escape do we have from the looming iceberg? This is the question that now presses on MPs with urgency, Labour MPs especially, the party leadership most of all. Rarely for an opposition, they can shape events. They can steer the country to safety. If they don’t, the ship of state is sailing towards catastrophe – and it’s getting nearer every day.

• Jonathan Freedland is a Guardian columnist