Chancellor George Osborne's plans to invest an extra £5 billion in new schools and other "shovel-ready" capital projects over the next two years will "make a difference" to the country, according to the prime minister.
The investment in schools, transport, science and skills - to be officially announced as part of Mr Osborne's Autumn Statement on Wednesday - will be partially funded by cuts in day-to-day spending by other Whitehall departments.
George Osborne makes his autumn statement on Wednesday
It will include £1bn to build or expand up to 100 new academies and free schools over the next two years, with the cash directed at areas experiencing a shortage in classroom places.
Mr Osborne and chief secretary Danny Alexander briefed Cabinet on the plans on Tuesday, which David Cameron said would "make a difference in our country and in our economy".
They said that the cuts in departmental spending amounted to less than the total of £3bn by which Whitehall departments have underspent their budgets over the past two years.
But Labour said the announcement was an effective admission that the coalition government's cuts in infrastructure spending since the 2010 election have been "a catastrophic mistake" which have weakened the economy.
And concerns were raised over the impact on services like the police and social care of cuts to current spending amounting to 1% (£950 million) in 2013/14 and 2% (£2.5bn) in 2014/15.
The chairman of the Police Federation of England and Wales, Paul McKeever, said forces were already having to cope with "crippling" 20% budget cuts before the "flabbergasting" announcement.
"We all accept these are austere times and savings need to be made but the police are already stretched to capacity," said Mr McKeever.
Meanwhile TUC general secretary Brendan Barber said the cuts would "put our stretched public services under even greater strain", while the £5bn additional investment was "nowhere near enough to undo the damage caused by £22bn of infrastructure cuts of the last two years".
Health, schools, international aid, HM Revenue and Customs and nuclear decommissioning will be protected from the latest round of cuts, while local government will be exempted for the first year and the Ministry of Defence will be given flexibility to carry over savings from previous years. The changes apply directly only to England, but will have a knock-on impact on devolved administrations.
The decision to inflict further cuts on Whitehall budgets comes after a mid-term spending assessment carried out by Mr Alexander, which found that departments have outperformed their savings targets since the 2010 general election.
David Cameron and Nick Clegg visited Corpus Christi Roman Catholic Primary School in Brixton, London
Speaking on a visit to a south London school with deputy prime minister Nick Clegg on Tuesday, Mr Cameron said: "Government departments aren't actually spending up to their budgets. So I think we can say to them 'You've got to cut back some spending, including some unnecessary spending', and let's put that money into things that will make a difference in our country and in our economy - more roads, more school buildings, more infrastructure to make our economy work better, to make our country work better."
Labour's Treasury spokeswoman Rachel Reeves said: "The chancellor seems to have finally admitted that abolishing the Building Schools for the Future programme and his other deep cuts to infrastructure investment were a catastrophic mistake which cost jobs and weakened our economy.
"But this extra funding for new free schools will be smaller than the huge cuts he made two years ago to school and college buildings. And George Osborne must explain which frontline services, like the police and social care, he will cut further to pay for this latest U-turn."
Conservative sources retorted that capital spending as a percentage of GDP will be higher during this Parliament than the average under Labour.
Mr Clegg said the announcement was about "making sure that the money we do have available to us is used for the best possible purposes - not tied up in Whitehall but used to rebuild schools, to improve our transport infrastructure, to invest in the things that this country needs for the long term."
CBI director general John Cridland said ministers were right to "squeeze every last penny to boost growth" and called on Mr Osborne to harness the spirit which delivered a successful Olympics to build vital national infrastructure, like improvements to the A14 and A303 trunk roads and a new relief road for the M4.
"Capital investment has the biggest impact on growth and getting our economy moving, so it's right to shift the focus from current spending, without borrowing more and deviating from cutting debt," said Mr Cridland.
Mr Osborne will also use his statement to signal his approval for up to 30 new gas-powered electricity power stations, as well as floating possible tax breaks and regulatory reforms to encourage investment in innovative "fracking" technologies for extracting gas from shale deposits.
Friends of the Earth denounced the policy as a "reckless dash for gas", and the GMB union said it was "madness" to burn more gas to produce electricity when wholesale prices were increasing.
But the Institute of Directors said gas will be needed until renewable energy sources become more reliable and affordable. Shale has the potential to supply a 10th of Britain's gas needs for a century, cut imports and create 35,000 jobs, said the IoD's Corin Taylor.
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