Philip Hammond only agreed to the NHS’s £20bn budget boost on condition that the service’s outspoken chief executive backed the deal, sources close to the deal have disclosed.

The chancellor made it clear in tense eleventh-hour negotiations that Simon Stevens had to publicly welcome the funding deal or he would not give NHS England as much money as Theresa May announced.

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Unless Stevens did so, Hammond would have handed the NHS a smaller percentage rise in each of the next five years than the 3.4% announced.

Stevens, a former adviser to Tony Blair in Downing Street, has taken issue publicly several times with the prime minister over exactly how much money the Conservative government has promised the NHS.

In January 2017, Stevens’s “stretching it” judgment in evidence to MPs that May’s claim her government was giving the service an extra £10bn generated extensive media coverage. Last November he also dismissed a £2.6bn cash injection in Hammond’s budget as too little, prompting anger in the chancellor.

“The deal was explicitly done on the basis that Stevens was required to support it. The chancellor said that if he was going to be pushed up [to a 3.4% increase] there would need to be a warm and effusive welcome for it. Stevens was in the room at the time Hammond said that”, one well-placed source disclosed.

“Hammond basically insisted that if he went as high as 3.4%, unless Stevens came out and publicly welcomed the deal he wasn’t going to budge on the number.” Stevens did not disagree with what was in effect the chancellor’s ultimatum, the source added.

When news of the £20bn package emerged last Sunday, Stevens welcomed it, saying: “As the NHS turns 70, we can now face the next five years with renewed certainty. This multi-year settlement provides the funding we need to shape a long-term plan for key improvements in cancer, mental health and other critical services.”

On Monday Stevens also welcomed the deal, but in different terms, when he answered questions from the Commons public accounts committee. “It represents a clear gear change in the amount of funding that will be available for the next five years, compared to what we have had over the last five years.” He used roughly the same form of words when talking about the settlement at an event hosted by the IPPR thinktank on Tuesday.

The NHS England chief’s public endorsement of the 3.4% deal is in stark contrast to his previous insistence, which he repeated to a gathering of health service bosses last week, that the NHS needed increases of at least 4% a year for the next few years.

Last week Stevens made clear that the government had received a lot of evidence on the service’s funding needs from independent bodies and should base the size of the increase on that. That evidence – from the Office for Budget Responsibility, Institute for Fiscal Studies and health thinktanks – all said the NHS needed rises of at least 4% in order to improve its performance against key waiting time targets and also expand services.

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His approval of the £20bn as enough to finance “key improvements” in priority areas of care is also at odds with the views of chief executives who run hospital trusts in England.

One, who did not want to be named, said: “The money we have got is more than a drop in the ocean, or a trickle, but it is hardly a torrent.”

The health secretary, Jeremy Hunt, has said the 3.4% deal will mean that taxes will have to go up. The deal has also led to May being criticised for talking “tosh” by a senior backbencher over her claim it will be partly financed by a “Brexit dividend”. The five-year deal will see NHS England’s budget rise from £115bn this year to £135bn by 2023-24.

Other chief executives, speaking on condition of anonymity, said that patients’ waiting times for A&E care and planned operations in hospital would continue to lengthen despite the extra money, a lack of beds and staff would see the service continue to struggle to cope with fast-rising demand and operations were highly likely to be cancelled again next winter.