So begins an epic waste of time and a monumental exercise in displacement activity. The Conservatives have taken a look at the scale of the crisis facing the country and decided their best response is to turn inwards and talk about themselves. With the Brexit clock ticking ever louder, they have retreated into the comfort zone to engage in their favourite pastime – a round of navel-gazing and internecine bloodletting.

We know how that time will be wasted. It’s already following the usual pattern, as multiple cabinet rivals to succeed Theresa May swear their public loyalty to the prime minister and insist that they will oppose the motion of no confidence in her leadership of the Conservative party when they, like their fellow Tory MPs, file into a Westminster committee room to cast their vote between 6pm and 8pm this evening.

May says new PM would have to delay Brexit if she loses confidence vote – politics live Read more

Before 9am today we had the traditional declaration of defiance from the beleaguered PM herself, Theresa May vowing to fight with “everything I’ve got”, echoing Margaret Thatcher’s 1990 promise: “I shall fight on, I shall fight to win.” (And we know how that worked out.)

If the vote goes against the PM and she is forced out, those same cabinet colleagues will then be free to campaign for her job supposedly unmarked by the stain of disloyalty. All the while, and also following tradition, Tory MPs will lie to reporters and to each other, promising support for this or that camp, support that they later withhold in the privacy of the voting booth.

Play Video 3:55 Theresa May: 'I will contest confidence vote with everything I've got' – video

So much for how the next hours or days might play out. What can hardly be disputed is that those hours and days will be wasted. For we are now just 14 weeks away from 29 March when, as a matter of law, the UK will crash out of the European Union. That is the legal default. That is what will happen unless and until parliament passes a law – either approving an exit deal or suspending article 50 – to avoid it.

It means that every second of those 14 weeks should be spent striving to come up with a plan of action that MPs could agree on, a plan that would avoid what all but the most dogmatic of hard Brexiteers admit will be the national catastrophe of a no-deal Brexit. It could be Norway plus. It could be a second referendum. But it has to be something. Otherwise we are heading off a cliff.

But instead of working day and night to avert that disaster, the Conservative party has decided to squander precious time with what several loyalist ministers are calling an act of self-indulgence. Not that the May camp can give any lectures about time-wasting. By delaying Tuesday’s scheduled “meaningful vote” on Brexit, the prime minister herself held up the essential process of elimination – rejecting the competing options one by one, until one is left – by which parliament might avert a no-deal exit. By holding up that process yet further, stretching it deep into January if May loses tonight and Tory members are balloted on a new leader, this latest move similarly takes us closer to the calamity of no deal.

But this is a waste of time in a deeper sense than merely using up valuable hours and days. It is also fundamentally futile. For the driving motive of those 48-plus Tory MPs who sought this vote is the belief that a change in party leader can bring about a different Brexit outcome. It cannot.

That is not because the EU is especially stubborn, and therefore unlikely to grant concessions to May’s successor that it withheld from her (though that is certainly true). It is rather that the facts themselves are stubborn.

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The justice secretary, David Gauke, was right when he told the BBC this morning that “the parliamentary arithmetic does not change if you change the person living in Downing Street”. As prime minister, Boris Johnson or Dominic Raab might dial up the Brexit rhetoric, but the numbers in the Commons will remain obstinately the same. It will still be a government without a majority. It will still be a hung parliament with a majority of MPs who backed remain.

More to the point, the Irish border question persists no matter who is in No 10. Under the Good Friday agreement, Britain is required to avoid a hard border between Northern Ireland and the republic. The EU is adamant on the same point, fixed in its view that there can be no hard border in Ireland, and yet equally certain that what would now be the external frontier of the EU necessarily involves customs checks and the like. No new PM will be granted a magic wand to wave away those facts, no matter how tightly they screw their eyes shut and insist they truly believe in Brexit.

Tory MPs don’t like hearing that they cannot have their cake and eat it, that there is no Brexit that comes without a severe cost, and so they are taking out their frustration on May. But any prime minister – Johnson, Davis, Raab, Mordaunt, Leadsom, Hunt, Javid – will eventually have to break the same news to them. The problem is not May. The problem is Brexit.

• Jonathan Freedland is a Guardian columnist