Figures from the Institute for Fiscal Studies reveal public spending could rise by more than 10%, providing a massive boost to the economy.
The news will add weight to the Local Government Association's argument that capital borrowing freedoms should be introduced as soon as possible to allow councils to invest.
LGA finance director Neil Kinghan said: 'Legislation should be brought forward to reform the local government capital finance system and improve investment in public services.'
The DTLR is one of the biggest underspenders. It underspent its main programmes by around£860m last year, according to the IFS figures. The Department for Education and Skills has underspent by around£1.4bn and the Department of Health by around£500m.
The IFS figures show departments are coming closer to spending the required budget, but there is still enormous scope for councils to be given greater powers to invest in vital services, according to the LGA.
Around£2bn worth of the government's capital expenditure, which is around 30%, has been carried forward into this year's spending plans. The total amount of underspend being carried forward is£6.7bn.
Senior research economist at the IFS Carl Emmerson said: 'There could be a huge increase in public spending, but it depends which departments are allowed to spend the budgets left over from previous years.'