They’re looking like the gang that couldn’t shoot straight. Labour’s upper echelon, both the prime minister and his rivals, have served up a performance of such political ineptitude, walking into doors and tripping over their own feet, that it’s hard to argue with the cabinet minister who glumly told me this was the week when the government did itself damage that can never be repaired, if not the week that Labour confirmed its defeat at the next general election.

As so often, the lead was set from the top. Keir Starmer’s allies had billed his speech on Monday as a major address, one that would meet the scale of the moment and recognise the need for Labour to chart a new course, given the shellacking the party had suffered at the hands of voters in England, Scotland and Wales on 7 May.

The text acknowledged it was time to banish the previous timidity, accepting that “incremental change won’t cut it”. And yet the speech was incrementalism itself. Its big new offer on Europe, for example, was not a declaration that in a world in which the US has become an unreliable ally or worse, the previous red lines, blocking British reentry into the customs union and single market, make no sense. Instead, it was the promise of a “youth experience scheme”. Everyone knows Britain has big problems that require big solutions, but this was small. Instead of dispelling the doubts about Starmer, it vindicated them.

And so, inevitably, it did not quiet the calls for a change of leadership. Wes Streeting had a favourable opening: with Andy Burnham absent from the House of Commons, this week was perhaps Streeting’s best chance. He made the preliminary moves, as allies resigned their posts, presumably hoping to trigger an avalanche that would eventually force the PM out of Downing Street. But the avalanche never arrived.

Streeting’s own resignation came without the backing of the 81 MPs required to initiate a leadership contest. Starmer’s camp were able to chirp the lyric from Hamilton in the former health secretary’s direction: “You don’t have the votes.” Streeting is meant to be a canny operator, who should have learned in his student organiser days that you make no move without the certain knowledge you have the support to see it through. But this looked like a rookie error. As one cabinet ex-colleague put it: “Wes has already made himself look smaller.”

For now, Burnham is the leader in waiting. But he too has messed up. His search for a way back to parliament has led him to Makerfield, where the local MP sacrificed his seat on Thursday so Burnham can contest it in a byelection. That will be a tall order, given the strength of Reform UK in that constituency: Nigel Farage’s party swept the board there in last week’s council elections.

Still, even some of Labour’s opponents on the ground reckon the Greater Manchester mayor’s personal appeal is strong enough to hold back the turquoise tide and that he will win the seat. If he does, runs the argument, he will have proven himself as the one Labour figure capable of taking on Farage and winning. Within days, Starmer will bow to that logic, resign and a swift, uncontested coronation of the king of the north will follow.

It might work. But Burnham’s gambit – and the future of this government – now rests entirely on the whims of the people of Makerfield. They may play the role assigned to them, or they may listen to the canvassers of Reform who will doubtless urge them to refuse to go along with the political games of the Westminster class, to take a stand against Labour’s sense of entitlement and its presumption that seats in parliament are property that can be handed from one mate to another. In such moments, I think of Boaty McBoatface and the tendency of voters, when given the chance to disrupt the plans of those in authority, to take it. (The historically minded will reach for the unhappy precedent of Patrick Gordon Walker, the Labour foreign secretary who needed to get back into the Commons in 1965 – only to discover that safe seats can become unsafe when voters feel taken for granted.)

If Burnham were to lose to Reform, Starmer would remain in place, but he would be terminally wounded and facing a Farage buoyed up by victory. Another bid would come before long, whether from Streeting or Angela Rayner or the underpriced Ed Miliband. And, in the process, Labour would have lost what had been its key appeal in 2024: the promise of dull stability after the chaos of the Tory years.

What, then, can the party do to mitigate the dire situation it now confronts? The first move is to make some lemonade from this barrel full of lemons. If Labour is entering a summer of introspection, it might as well use it. It should have the full-throated debate it has long avoided. The mistake it made with Starmer is the same mistake the Conservatives made as they chose serial prime ministers – opting for a blank canvas on whom they could project their often wildly divergent hopes. Labour must have a much fuller sense of exactly what a new PM would do and say in office.

Such a debate has to begin with understanding the depth of the hole the party is in, and therefore how great the leap that will be required to get out. That means thinking radically about taxation – as the party has surely learned, a mansion tax here or abolition of non-doms there cannot raise the revenue needed – but also about economic growth. Put simply, what’s needed is a detailed programme to get Britain making products that people around the globe want to buy, deploying all the resources government can muster to that end. Similar clarity is required on Britain’s place in a world transformed by Donald Trump and the breakdown of the post-1945 order. If a candidate can only speak about such things in platitudes, their path to Downing Street should be blocked.

In other words, though the folly of our system allows a relative handful of party members to pick a prime minister, Labour has to choose someone who does not merely tickle the party’s tummy, but can plausibly serve and then win over the nation. “Country first” is a hackneyed slogan, but that has to be the guiding principle. If Labour picks a candidate who delights only itself, it will lose.

It is a daunting job description. Labour is looking for someone who can do all of the above and is a gifted communicator to boot. Anything less will not be good enough. Labour is about to undergo a search for a new leader of the United Kingdom. It should approach that task with the seriousness it deserves, free of the clown-show antics that have characterised the comings and goings in Downing Street for a decade. If Labour is to pick the seventh British prime minister since 2016, it had better get it right – or else the eighth will wear the irremovable smirk of Nigel Farage.

• Jonathan Freedland is a Guardian columnist