Services and departments that have not been promised protection in the pre-Budget report face cuts of more than six per cent, the Institute for Fiscal Studies (IFS) has calculated.

Ministerial assurances that overseas development, health, 'frontline' schools and Sure Start will either see increases or have their budgets frozen means other departments' budgets will be cut by 6.4 per cent between 2011 and 2013.

Chancellor Alistair Darling has refused to set out the financial future for individual departments, but IFS senior research economist Gemma Tetlow believes significant unprotected areas are defence, higher education, transport and housing.

The research institute, which published its appraisal of the pre-Budget report on Thursday, also identified a £15bn hole in the government's plans for where savings would be made.

Overall, the government wants £35.7bn to be saved by 2013/14. But the £12bn in efficiencies, £1bn in public sector pension reforms, £5bn cut from low-priority budgets and £3.4bn from tighter control over public sector pay only comes to £21.4bn.

The IFS report also notes that the National Audit Office has questioned the government's record on efficiency savings. In a report on the 2004 spending review period it could only endorse 25 per cent of the claimed efficiency savings, and was unsure whether the remaining 75 per cent had been demonstrated.

By the government's own calculations, Tetlow added, it still had £26.5bn of efficiency savings to deliver within this spending review period which ends in 2010/11.