John Healey, the former Treasury minister appointed by Jeremy Corbyn as shadow housing minister, will say on Monday that the state could build 100,000 new council houses and housing association homes a year to drive down the UK’s spiralling housing benefit bill and tackle the affordability crisis.

It would involve almost quadrupling the current number of affordable homes being built. Healey, who has previously said his priority is the decline in home ownership, proposes the homes should be for sale as well as rent.

Corbyn made housing one of the totemic issues in his campaign for the Labour leadership and he has since said it is a top three policy priority. The proposal, which is not yet official Labour policy, represents a marked change from Ed Miliband’s stance. He campaigned with a pledge to build 200,000 homes a year, without saying how many of those would be for private sale.

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In his report for the leftwing Smith Institute thinktank and with the accountancy firm PricewaterhouseCoopers, Healey estimates that 100,000 homes a year could be built by 2020, costing the government £13.5bn. He says this would lead to a net £5.8bn saving because of reduced housing benefit costs.

Among the funding measures are £1.8bn a year in grants to enable 30,000 homes a year, looser restrictions on councils borrowing against their assets, delivering 60,000 homes, and forcing private developers to build another 16,000 homes a year as part of planning deals.