The Department of Health has already said it wants efficiency savings of 4% for each of the next five years.
But the regulator Monitor says it expects savings will be more in the order of 6% to 7%.
Monitor says higher than expected inflation and tougher financial penalties for hospitals are to blame.
As part of the government's reforms of the NHS in England every hospital is expected to become a foundation trust.
But to do that they must satisfy the financial regulator they can balance their books.Efficiency savings
About 85 hospitals and mental health trusts have yet to achieve foundation status, but now Monitor has told them the bar is being raised even higher.
In December the Department of Health said it was looking for efficiency savings of 4% for each of the next five years.
But in a letter to foundation trust applicants, Monitor says that higher than expected inflation, plus tough financial penalties for things like emergency re-admissions after surgery, mean savings will need to be between 6% and 7%.
In a statement the regulator said the changes to the economic climate meant all trusts would need to make savings.
"However, we should be clear that these assumptions are a reflection of the risks in the external environment; they are not a directive to make cuts.Continue reading the main story
I can see a hospital doing this for one or two years, but not five years”End Quote John Appleby Chief Economist, The King's Fund "Trusts will need to take account of the individual circumstances that exist within their local health economy, which could mean that they will need to take either a more optimistic or pessimistic approach than the one set out by Monitor.
"It is essential that the quality of patient services does not suffer as a result cost-cutting measures."
In a statement the Department of Health said Monitor's assessment would be "challenging" for the NHS but pointed out that it was the "more pessimistic" of two scenarios set out by the regulator.
"The NHS is in a strong financial position. We are investing an extra £11.5 billion into the NHS by 2014-15.
"But higher costs and an ageing population mean that the NHS must meet the highest possible financial standards and find savings to reinvest into patient care.
"Monitor's assessment of 6% to 7% is its 'downside case', meaning it is more pessimistic. But it is right that Monitor's assessments are challenging - we want all hospitals to be able to meet Monitor's standards and show that they can provide sustainable, high quality and efficient services for their patients."Benchmark
These figures matter not just because they show the financial pressures on the health system and in particular on hospitals.
They are also the benchmark which Monitor will use to judge whether a hospital will be granted foundation status.
And while some health economists had questioned whether hospitals could make year on year savings of 4%, these new figures look much tougher.
John Appleby, chief economist at the health think tank the King's Fund, said the savings were a big increase.
"I can see a hospital doing this for one or two years, but not five years.
"It's like the unit cost of a hip operation, around £6,000, has got to decrease by 37%. How?"
Shadow health secretary John Healey said: "This confirms the combination of broken promises on NHS funding and reorganisation is putting a huge strain on hospitals. David Cameron must halt his high-risk, high cost overhaul of the NHS."
Hospitals in England have until April 2014 to achieve foundation trust status.
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