The NHS will end up with a £65bn hole in its finances by 2030 unless ministers plug the gap or allow the quality or availability of care to slip, say health economists.

The Health Foundation analysis identifies the sum as the extra amount of Treasury funding the NHS will need by then because it is unlikely to meet unrealistically optimistic productivity targets.

It says the NHS will need its budget to rise by 2.9% a year above inflation each year between 2015-16 and 2030-31 if it is to maintain the standard of services and avoid having to ration access to treatment.

That 2.9% is higher than the expected 2.3% annual rise over that period in gross domestic product, which means the government will have to boost NHS spending faster than the economy is growing.

The £65bn will also be needed because the health service is likely to make only 1.5% annual gains in productivity and not the 2% and 3% envisaged in the Five Year Forward View, NHS England’s recent blueprint for securing the service’s uncertain future.

The Health Foundation wants whoever forms the next government to make reaching “a public and political consensus” on the NHS’s long-term funding needs a priority, and also to give it further additional money from April as a “transformation fund”, so new ways of delivering healthcare can be created.

“The next government will have to act immediately in order to secure the future of the health service in years to come,” said Anita Charlesworth, the thinktank’s chief economist.

Frank Dobson, Tony Blair’s first health secretary after his election victory in 1997, has blamed the current overcrowding in A&E units on the government spending too little on the NHS and investing too little in services outside of hospitals.

“If we want a first-class healthcare service, we’ve got to pay a first-class fare and we aren’t paying a first-class fare, we’re paying 10% of our national wealth on health,” he told London Live.

Andrew Gwynne, the shadow health minister, said: “The only way to make the NHS affordable and sustainable in the 21st century is to fully integrate it with social care, as Labour plans.

“In addition, we have committed an extra £2.5bn a year over and above anything we inherit from the Tories. David Cameron has failed to pledge the extra money the NHS needs in the next parliament while the Liberal Democrats have made entirely unfunded plans, the very last thing the NHS needs right now.”

Andy Burnham, the shadow health secretary, plans to set out Labour’s plans for the NHS next week.

A government spokesperson said: “While we welcome debate on the long term future of health finances, given the economic uncertainties with projecting ten or fifteen years out, the NHS’s focus is understandably mainly on the next five years as set out in the NHS Five Year Forward View.”