One of Labour’s triumphs in the 2017 election was the popularity of its “fully costed” manifesto. But a new book reveals that Jeremy Corbyn’s top aides, including Seumas Milne, his director of strategy, feared the party’s spending plans would unravel during the campaign, but were overruled by John McDonnell, the shadow chancellor.

A book to be published tomorrow reveals the existence of an internal email before the launch of Labour’s manifesto that “highlighted some of the problems with Labour’s cost estimates, including the lack of detail on capital spending, as well as some individual costings that were implausible or entirely absent”.

At the time, the manifesto was well received, and the short document setting out the costs of Labour’s promises and how they would be paid for, “Funding Britain’s Future”, was widely accepted. Labour were helped by the Conservatives’ refusal to provide costings for their manifesto, which allowed Corbyn and McDonnell to contrast the government’s plans with their own “fully costed” proposals.

Privately, however, their staff had told them their figures didn’t add up. The email identified problems with “almost every area of the manifesto, including welfare, health, education, the economy, transport, policing and prisons”, according to Philip Cowley and Dennis Kavanagh, authors of The British General Election of 2017, the latest in the respected series of academic election books. The email estimated, “even conservatively”, that the manifesto implied “billions of unaccounted spending”.

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According to Cowley and Kavanagh: “A prolonged debate including all those around Corbyn and McDonnell as well as longstanding senior party staff was ultimately resolved at McDonnell’s insistence, despite the fears of several of Corbyn’s aides, including Seumas Milne.”

One source quoted in the book said: “There were people there who were long in the tooth enough to remember John Smith’s shadow budget in 1992.” Plans set out by Smith as shadow chancellor were attacked by the Conservatives as a “tax bombshell” and were widely thought to have helped Labour lose that election. But this time McDonnell decided Labour were so far behind that “there was nothing to be lost”.

All the same, the book also reveals the shadow chancellor was too cautious for a bold plan, proposed by Krow, the party’s communications agency, to take up the promise made by the Leave campaign in the 2016 referendum of an extra £350m a week for the NHS. “A Krow proposal to hire the bus used by the Leave campaign in the EU referendum and have it decorated with the promise of £350m per week for the NHS impressed McDonnell,” the authors say. “He was keen to do it for the local elections, but ultimately backed away when his team could not convincingly make the sums add up.”

This is surprising, because Theresa May herself co-opted that pledge earlier this year, using Treasury numbers to promise an extra £384m a week for the NHS by 2023.

The book also contains new information about Labour’s planning for a range of possible election outcomes. Early on, when it looked as if Labour would lose so badly that Corbyn would have to stand down, there was some planning to prevent Tom Watson, Corbyn’s deputy, from taking over as acting leader.

The book says: “The plan would have been to announce a timetable for his resignation, but with his staying in post until a new leader was elected at the party’s annual conference. The aim was to stop Labour’s deputy leader taking office, even as an interim position. ‘We did not want Tom Watson becoming acting leader’, said one of Corbyn’s closest aides.”

Later, as Labour started to do better in the opinion polls, most of the planning assumed that the party would gain a greater share of the vote than Ed Miliband, allowing Corbyn to claim an advance and that he should stay on as leader.