Whitehall goes into purdah pondering two big questions and a teaser, assuming Theresa May wins big on 8 June.

The teaser is how long it will be before a successor to cabinet secretary Sir Jeremy Haywood is sighted. He is not going to go on for the length of a parliament; he isn’t a member of her Praetorian guard and the job isn’t what it used to be.

More significant, for the public service, is how soon after 8 June might No10 roll back austerity, undoing the March budget, in order to accommodate both Brexit and (to be revealed in the Tory manifesto) May’s own “vision”?

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The other challenge is whether a victorious May would give the machine the direction and momentum it has obviously lost. In part that would mean increasing staff numbers, pay and pensions. But it also depends on whether May comes back convinced that beefing up the civil service is a precondition formaking Brexit work. That’s not just bodies but equipping the machine to map, conceptualise, structure the future of the country and the state.

Among other things that would mean – back to Heywood – refocusing the centre of the centre and reworking the boundaries between Cabinet Office, No 10 and the Treasury. That points to something resembling a strategic training and staffing function.

MP Bernard Jenkin, a leading leaver, and his colleagues on the Commons public administration and constitution committee have just had a go at the lack of forecasting and preparation that has left the system scrambling, making hurried appointments and paying consultants for expertise they may not have.

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Yet if Jenkin believes in planning, few of his Tory colleagues appear to. Under Cameron and, so far, under Theresa May, the idea of government mapping, conceptualising, structuring the future – even its own future in terms of institutions and capabilities – has been derided and rejected. If there’s any planning of civil service futures going on, it will be cabinet secretary Sir Jeremy Heywood secretly poring over an Excel spreadsheet in the dead of night.

Even then, his tools for executing any plan are limited. It’s not just austerity, continuing staff cuts or the dogmatic insistence on capping civil service pay even for the most prized skills, it’s also the absence of anything in Whitehall that resembles a strategic training and staffing function.

The subtitle to the OECD’s recent report on national schools of government is “building civil service capacity”. But we do not have a national school of government. Francis Maude, civil service minister under Cameron, has lately been feted by the Institute for Government as a great reformer, thwarted by stick-in-the-mud permanent secretaries. That’s far from the whole story. Whatever else he did, Maude swept away the puny residual of Whitehall’s capacity to teach itself, to mobilise internal expertise for the sake of upskilling recruits.

The story is well worn. Labour prime minister Harold Wilson wanted to modernise Whitehall. The commission he appointed led by Lord Fulton recommended a well-resourced civil service college. The machine responded grudgingly, but for a few years central government had a pan-departmental training and thinking capacity, lodged in a plush park at Sunningdale in Berkshire.

The Thatcherites whittled away at the college. Labour established the Centre for Management and Policy Studies in the Cabinet Office, which looked for a few brief months as if it might energise skills, training and internal intellectual capacity. The civil service college was rebadged the National School of Government, but became a fee-paying academy and departments ceased to bother. It withered, until Maude cut off life support. Training was privatised. Capita became – somewhat paradoxically – responsible for instilling the ethos of public service.

The OECD, dependent on funding from member states, avoids direct criticism but can’t conceal the fact that the UK is an outlier in training its civil servants. Looking across the west, the OECD’s public sector chief, Rolf Alter, sees a mixed picture, but most countries have something resembling a national school. Some countries even have “national learning strategies” for their entire public sectors.

National schools of government will be the places to help states reconnect and regain public trust and assent to taxation, the report argues.

Perhaps a national school will have to be reinvented. The Cabinet Office isn’t happy with the dog’s breakfast that is Whitehall’s arrangements for capacity building and skills training. Its instinct is to outsource. Discussions are going on with universities, among them King’s College, London about providing management education for officials. But we’ve been down that road before and master’s degrees in public administration have never really taken off.

Maybe this time, because of Brexit, the medium- to longer-term shape of the state is in play. Even if the predominant civil service role is going to be picking up the pieces, it will take knowledge and dedication, which a national school of government could create and share, and push back a little against the strong centrifugal force of departmentalism.

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