The NHS is "off target" with its efficiency plan, a health research charity has said.
The Health Foundation comments come after NHS England released a technical briefing note abut efficiency savings.
In 2014 the national health body said that the NHS would have a £30 billion funding gap if current demands for healthcare continued, funding remained flat in real-terms and no further efficiency savings were made.
In the Spending Review (SR), delivered in November last year, the Government said annual funding for the NHS in England will rise by £3.8 billion above inflation in 2016/17 and £8.4 billion above inflation in 2020/21.
The NHS England document states: "While this implies an efficiency requirement of £22 billion by 2020/21, the majority of these efficiencies are not cost reductions per se, but action to moderate the counterfactual rate of spending growth.
"Furthermore the SR assumes that around £7 billion of the total will be delivered nationally, leaving only £15 billion to be sourced locally, of which under £9 billion would come from conventional provider productivity.
"This scenario requires a 2% annual efficiency gain from providers; this was partly based on efficiency work produced by NHS Improvement, which concluded that this level of efficiency was stretching but achievable."
But the Health Foundation said the briefing note shows the NHS delivered savings of just £1 billion last year.
Anita Charlesworth, director of research and economics at the health charity, said: "Today's briefing by NHS England is a welcome focus on where the NHS expects to achieve efficiencies over the remainder of this Parliament.
"(Some) £15 billion of savings from local NHS services are required if the national target of £22 billion is to be met by 2021/22.
"However, by its own estimate, the NHS delivered savings of just £1 billion towards this last year, confirming that the health system is substantially off target with its efficiency plan. At its heart, this reflects fundamental weakness in the approach to efficiency in the NHS - too much reliance on one-off savings.
"What is now crucial is a comprehensive plan with clear accountability for how these savings can be achieved in reality. Patients and the public also need assurance that these savings will be genuine efficiencies and not simply reductions in quality."
The briefing note was published as NHS England boss Simon Stevens and Health Secretary Jeremy Hunt appeared before the Commons Health Select Committee.
Committee chairwoman Dr Sarah Wollaston asked Mr Hunt about the amount of money promised in the Spending Review.
Dr Wollaston said: "Can I comment on the £8.4 billion promised in the Spending Review, which is £7.6 billion if we look at it in 15/16 prices, and also the fact that it appears to have been redefined as spending on NHS England, rather than the usual baseline. So it appears to us that it is £4.5 billion of new money."
She added: "Would you recognise that the figure is actually £4.5 billion?"
Mr Hunt said: "I recognise that we are talking about £8 billion that was needed for NHS England to deliver the Five Year Forward View and that in order to deliver that we have had to make some difficult efficiency savings in the rest of the health budget.
"I do recognise that we didn't protect the entire health budget.
"But our determinant as to whether this was sufficient was what NHS England felt they needed in order to put in place the Forward View. And yes, we are making very challenging efficiency savings in the non-NHS England part of the health budget. But I think it's right we do so in that we are asking NHS providers to make very challenging efficiency assumptions, the £22 billion, so I think that it is reasonable that we should also ask other parts of the health budget also to make those savings.
He added: "We are looking for savings that don't impact on patient care."