The government should make its funding for housebuilding more flexible to prop up the construction sector and deliver more homes throughout any Brexit-triggered slowdown, says a group representing housing associations across the country.

A report by the Centre for Economics and Business Research (Cebr) consultancy, commissioned by the National Housing Federation (NHF) and the Chartered Institute of Housing (CIH), suggested loosening the rules for funding availability for housebuilding.

Currently, there are billions of pounds in public money available to support specific types of housebuilding. For example, the government has set aside £2.3bn ($3.01bn) specifically for the construction of discounted "starter homes" for first-time buyers, its flagship homeownership policy introduced under the controversial Housing Act earlier this year.

But the NHF argues that allowing housing associations to access such money based on their own decisions of what types of home need to be built in certain areas, turning it into a loose general fund worth as much as £7bn, will boost housebuilding and the wider economy. It would mean the government abandoning specific targets for building certain types of property, such as starter homes, and instead focusing on its broader target of a million new homes by 2020.

This is especially important after the vote for Brexit, argues the NHF, because where market-sensitive private housebuilders retreat, housing associations can advance. Some economists expect the UK economy to slip into recession as firms pull investment amid the Brexit uncertainty.

Weaker consumer confidence and tighter credit conditions could hamper housing demand, in turn causing private housebuilders to rein in construction work — hurting efforts to solve the country's protracted housing crisis. Housebuilding is running at around half the level needed to meet demand. After the 23 June referendum, housebuilder shares collapsed.

Housing associations can plug any potential gaps in output and ensure homes of all types are still built, construction supply chains remain intact, and skilled labour does not leave the sector en masse as happened after the financial crash of 2008, leaving a serious skills shortage. For every billion pounds of public money spent, the NHF believes housing associations can deliver 33,000 new homes. They would inject the bulk of the funding from their own surpluses and borrowing.

"The warning signs are flashing amber – housebuilding may be set for a slowdown – but housing associations have a track record of building through tough times," said David Orr, chief executive of the NHF. "Demand for good quality rented homes remains high.

"Today, the sector puts forward a plan of action for the prime minister to keep the nation building and tackle the housing crisis. It is a plan that comes at no extra cost to the taxpayer and one that will improve the life chances of hundreds of thousands of working people in this country. Uncertain times call for pragmatism and flexibility."