Primary care trusts and council social care services will share an extra £162m this year thanks to a Department of Health “efficiency drive”.

The DH said PCTs should hand the money to local authorities but agree with them how it should be spent on helping people leave hospital more quickly and avoid readmission.

It said the funds came from “efficiency savings [from] applying the controls over central spending on consultancy, IT, administration and advertising [which are] common across all of government”.

The £162m is on top of £70m announced for the same purpose in October, and the DH has said more funds will be directed in the same way in coming years.

The announcement comes after the leak of a letter, apparently revealing further concern within government about DH policy, including that the NHS may fail to save enough through efficiency to avoid an “unpalatable” trade-off “between dealing with the fallout from increased waiting times or increasing the DH budget, perhaps by as much as £10bn a year”.

The letter leaked to the Guardian was from members of the Cabinet Office’s Independent Challenge Group, set up to help with the comprehensive spending review settlement process, and addressed to chief secretary to the Treasury Danny Alexander.

Dated 7 September the letter said plans for savings under the quality, innovation, productivity and prevention programme, “may not be achievable”. That, along with the “costs of the switch from PCT to GP commissioning, mean the NHS “could therefore face a significant budget shortfall by the end of the SP [spending period]”.

The letter recommends, “the DH settlement needs to build in much greater non-QIPP efficiency savings from the outset”.