When a Conservative minister arrives in the offices of a newspaper or broadcaster, they’ll often see the faces of friends, ex-colleagues or even horseriding chums. It’s the same in the City, the same for business, the same across the thinktank world. Because of this it can seem, from the inside, that the party has dense roots and political resilience. And as long as you’re talking only about this elite horizontal stratum, it does.

But the resignation of Iain Duncan Smith shows the fragility of the project. Cameron became prime minister with the support of just 24.3% of registered voters. The recovery has petered out. The fiscal rules are broken in their entirety. There is every possibility that Osborne will be forced out; that Cameron will be challenged; that Brexit will happen, triggering a new election; and after that, a second Scottish independence referendum.

Labour’s frontbench can notch IDS up as a tactical victory: they prepared their own fiscal rule, pitched their budget response around Osborne’s failure and lack of fairness, and conducted themselves competently. As a result, they have probably killed off Blairite dreams of a coup, even if some of the plotters continued on autopilot, attacking their own leadership while the Tories imploded.

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But now, to become ready for government, Labour has to make hard choices – and in areas the radical left has little experience of: party management, political strategy, and compromise with one’s own principles.

Corbyn has the firm support of most unions, tens of thousands of new and active members and about a quarter of the PLP. His enemies are isolated. But his real problem is the unenthusiastic centre: the legion of Labour councillors swept up into Osborne’s “Northern Powerhouse” farrago; the centrist Labour MPs who just want to win; and, above all, the swing voters waiting to see what Labour becomes under Corbyn.

Given the urgency, and the soreness of political wounds, there is an obvious solution: for Corbyn to make an explicit offer to the right and centre of his party that allows them space, gives them responsibility and even allocates them control of certain policy areas. In return he – and the party membership – should ask that they turn their Twitter accounts and millionaire-funded private offices against the Conservatives, not the left.

Corbyn might have to face down resistance to that from some in the Momentum group, whose activists believe over the long term they can transform the entire party. That may have been true over a five-year opposition term, but Labour now has to plan for a shorter turnaround.

Labour’s strategic problem is that the tribes on which its traditional alliance has been based are fragmenting. Scotland is gripped with a radical cultural nationalism that Labour’s remaining members there have trouble relating to. Large sections of the old, white working class want out of Europe. The urban salariat of cities and large towns identifies with the Corbyn brand, but is not big enough, without the other tribes, to win an election.

And Labour’s support within the 1% is minimal. This matters. Greece showed that if you are to become the first left government of a major country to reject free-market economics, you need expertise: trained lawyers, technocrats, administrators and economists.

The urgent policy issues for Labour are defence, industry, Scotland and welfare. It needs to bury its differences on Trident around a solution that involves both wings compromising on their principles. It needs to go beyond discussing industrial policy to quickly designing one. And it needs to take a position on the Scottish national question.

Under the leadership of Kezia Dugdale, Scottish Labour is trying to outflank the SNP to the left while assuming the issue of independence to be closed by the Scotland Bill. On the Scottish doorstep, that’s not playing well. As a result, there is a wing of Scottish Labour that is now prepared to countenance what Gordon Brown would not: full fiscal autonomy, a federal UK and a new relationship to the English party resembling that of the CSU to the CDU in Germany.

But as he tries to reforge Labour as an alliance, Corbyn will have to manoeuvre around the same iceberg that sank IDS: welfare.

Even last year, only 48 Labour MPs voted against the household welfare cap. Many of the methods IDS deployed against claimants – means tests, fitness tests, coercive interviews – were pioneered under Labour. Conversely, the one good idea Duncan Smith had – universal credit – only works if you fund it properly and mend the implementation shambles surrounding it.

So, Labour’s biggest offer has to be a redesigned welfare state. This will be hard to design in a single conference season, while some of the sharpest minds on welfare are in that group of MPs that has decided not to participate in the Corbyn team. An overt offer of responsibility to them might change that.

Labour can emerge as a new kind of left social-democratic party – an alliance of different projects rather than a monolith. It would be led by the radical left, but make space for a loyal social democratic centre and a devolved Scottish party. It’s not the Labour party we knew. Nor is it exactly the one Corbyn’s supporters dream of creating by 2020. But faced with a disintegrating government, we need a Labour party united and ready to govern.