The Department of Health has been warned that without a new injection of government money hospital waiting times could increase as planned efficiency savings "may not be achievable".
The Guardian reported that a letter from the independent 'Challenge' group – established as part of the government's spending review process – said the department could be left with an "unpalatable" choice between seeking extra money or cutting services.
The Department of Health claimed that the letter, sent in September, before the government completed its spending review, was out of date and that the issues mentioned had already been dealt with.
But Labour said it demonstrated that Health Secretary Andrew Lansley was in charge of a "rogue department" and urged Mr Cameron to take action to get it back on track.
The letter, sent to Treasury Chief Secretary Danny Alexander, questions whether promised quality, innovation, productivity and prevention (QIPP) will achieve efficiency savings, as well as raising concerns about the cost of the switchover to the government's flagship policy of GP commissioning.
"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," it said.
"The government will be faced with a choice between dealing with the fallout from increased waiting times or increasing the DH's budget, perhaps by as much as £10bn per 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 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 spokesman said the concerns raised in the letter were no longer relevant.
"This letter was part of the process of independent challenge in the spending review," the spokesman said.
"The work has now concluded and the letter is therefore out of date - it has been overtaken by publication of the response to the white paper consultation and primary care trust allocations for next year."
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