Theresa May will have to rip up the government’s financial plans for the NHS and commit more than the promised £8bn extra by 2020, a hospitals boss has said.

Chris Hopson, the chief executive of NHS Providers, said ministers must come up with a new plan to fix the health service’s crumbling finances or risk it becoming unable to function properly.

In a submission to the Treasury before next week’s autumn statement, NHS Providers, which represents 96% of NHS trusts in England, says a rethink is necessary because the calculations underlying the government’s £8bn pledge are flawed.

It says demand for care is rising faster than envisaged in the blueprint drawn up by NHS bosses in 2014, the Five-Year Forward View, and social care has deteriorated.

Hopson said: “Some of the key assumptions in the Five-Year Forward View, on which the current financial and NHS delivery plans for this parliament are based, have turned out to be wrong. There is now a clear and widening gap between what is being asked of the NHS and the funding available to deliver it.

“The NHS simply cannot do all that it is currently doing and is being asked to do in future on these funding levels.”

Andrew Lansley, the health secretary from 2010 to 2012 in the coalition government, recently said the NHS needed a “Brexit bonus” of £5bn on top of the £8bn already pledged, given the widespread public demand for higher NHS funding revealed by the EU referendum.

NHS Providers does not specify how much more it wants invested. But Hopson said more than £8bn was justified because “demand for care is a lot higher, social care is in a much worse state, general practice is turning out to be more unstable, and the starting point for the deficit among hospital, mental health, community and ambulance trusts has turned out to be much larger.”

He said the overall health budget would go up by only £4.5bn by 2020, not the £8bn ministers pledged last year, because money was being taken from key areas such as public health in order to give the NHS its promised increase. Independent experts agree £4.5bn is the true increase that healthcare will get.

The NHS’s inability to deliver the £22bn of savings it had promised to make by 2020 – a target that had always been “too ambitious” – further underlined the need for more money to be found before the end of this parliament, said Hopson.

May has been under pressure recently over her repeated claims that the government is giving the NHS £10bn more, and more than the NHS England chief executive, Simon Stevens, asked for in 2014. Sarah Wollaston, the Conservative chair of the Commons health select committee, and other members of the committee wrote to the chancellor Philip Hammond to say the claims were untrue. Labour has asked the UK Statistics Authority to rule on whether the £10bn claim is justified.

Jeremy Hunt, the health secretary, has subtly distanced himself from the £10bn figure and said the NHS will need a lot more money after 2020, at the end of its unprecedented decade-long budget squeeze.

Ministers have already told Stevens that the NHS will not receive a funding boost in the autumn statement. But NHS and local council leaders hope the chancellor may find some extra money to prop up the ailing social care system.

“NHS funding increases from next year onwards are not enough to maintain standards of care, meet rising demand from patients and deliver essential changes to services,” said Richard Murray, director of policy at the King’s Fund thinktank.

“If additional [NHS] funding is not forthcoming later in the parliament, the government will need to be honest with the public about the impact on quality of care and access to services.”

The Department of Health did not respond directly to Hopson’s comments. A spokesman said: “This government has taken tough economic decisions that have allowed us to invest in our NHS, which is meeting record patient demand whilst improving standards of care. We have prioritised funding for the NHS with £4bn extra this year.”