A "complacent" Department of Health will face an annual £10bn shortfall unless it speeds up efficiency savings across the NHS and considers cuts to social care and cancer research charities, according to a secret Whitehall report leaked to the Guardian.

The damning report warns that ministers will face an "unpalatable trade-off" between longer waiting times or a massive increase in the NHS budget unless dramatic savings are found.

It also warns that the central reform proposed by health secretary Andrew Lansley – to devolve 80% of the NHS budget to GPs – could have "patchy" results.

The findings are outlined in a blunt letter to Danny Alexander, the Treasury chief secretary, from the Independent Challenge Group, which was set up at the time of the budget in June to question Whitehall thinking.

The letter, leaked as David Cameron expresses private concerns at Lansley's failure to drive reforms, quotes a senior Department of Health official outlining the scale of the challenge. The proposed changes are "greater and more rapid than those achieved in any national health service in any country in the past," the official said. But the group showed impatience with the department when it warned:

• Proposed savings under the Quality, Innovation, Productivity and Prevention (QIPP) programme "may not be achievable". This is due to account for the bulk of the £16bn annual efficiency savings the department needs to make by 2014-15.

• The benefits from the transference of spending powers to GPs will be variable. The letter says: "We fear that the results will be patchy with some commissioning consortia performing very well, but others performing poorly, again reducing the pace of overall cost benefit realisation."

• Ministers will have to consider "even greater" cuts to the social care budget than a so far unannounced £3.4bn in service cuts because £2.2bn of efficiency savings "must be in doubt".

• The NHS cannot afford to spend up to £200m a year supporting research by big charities such as Cancer Research UK.

• The government should scrap the "very bad policy" of employing all doctors when they graduate.

The letter says the costs of meeting the current level of demand for healthcare will rise from £100bn to around £115bn a year by 2014-15. But a combination of new policies and an ageing population will increase that to £126bn a year. With the budget due to rise at least in line with inflation to roughly £110bn a year, efficiency savings of £16bn a year will be needed. The reforms are expected to bring £6bn of savings, leaving a £10bn shortfall.

In its letter, the Independent Challenge Group warns: "We believe that the projected level of QIPP savings may not be achievable. We also have concerns about the costs of the switch from PCT [primary care trusts] to GP commissioning; and the pace at which the associated benefits will be achieved; and about the impact on NHS costs of the planned cuts to the social care budget – which DH only intends to add to its submission once the funding gap is clear … Taken together, the NHS could therefore face a significant budget shortfall by the end of the SP [spending period].

"The NHS typically deals with such shortfalls by limiting treatments, leading to increased waiting times. The government will be faced with a choice between dealing with the fallout from increased waiting times or increasing the DH budget, perhaps by as much as £10bn a year. To avoid this unpalatable trade-off, the DH settlement needs to build in much greater non-QIPP efficiency savings from the outset."

The letter has been leaked as Lansley faces intense pressure to prove that he can deliver his reforms to transfer commissioning powers to GPs. Cameron recently spoke to Lansley to push him on his planned efficiency savings, and coalition policy chief Oliver Letwin has been tasked with examining Lansley's plans to shift power to GPs.

Cabinet Office sources voiced concerns about a "complacent" attitude in the Department of Health towards QIPP, introduced by the last government, which could jeopardise Lansley's GP reforms.

A source said: "Ministers are very worried that the Department of Health does not seem to be taking it seriously. The risk is that if there is a cash problem in the NHS it will be blamed on Andrew Lansley's reforms, when actually the problem is a lack of will on efficiency savings."

The Independent Challenge Group makes clear that ministers will have to consider tough savings, including in social care, because of varying levels of efficiencies among local authorities. "Even the planned £2.2bn of efficiency savings must be in doubt, leading to fears of even greater service cuts," the letter says.

The letter was written on 7 September by the former APAX chief investment officer Adrian Beecroft, the chief executive of the Legal Services Commission, Carolyn Downs, and the director of climate change adaptation at the Department of Energy and Climate Change, Robin Mortimer.

A Department of Health spokesperson said: "The independent challenge group was established as part of the spending review process. The points raised by the group were considered as part of the spending review process. Its work has now concluded. We consulted on our reforms and received a huge number of responses: over 6,000. These have helped us to refine our plans. We have responded to concerns around implementation and are testing several areas of reform to make sure we have the best arrangements in place.

"GP pathfinders are already leading the way to making our reforms a reality, with 52 of them taking on commissioning responsibilities and testing consortia arrangements. More will follow. They demonstrate the level of enthusiasm in the system for taking these ideas forward. Many GPs are ready and willing to take on commissioning responsibilities so that they can improve services to better reflect the needs of local communities."

John Healey, the shadow health secretary, said: "This document is extra evidence that the high-risk, high-cost reorganisation Andrew Lansley is forcing on the NHS is a massive distraction from improving patient care and making the sound efficiency savings Labour previously planned.

"It also confirms concerns that the health secretary is running a rogue department and operating in isolation from his ministerial colleagues. For the sake of patients and the future of healthcare, David Cameron needs to get a grip on his government's NHS plans."