Labour has pledged to build a million new homes over five years, if its wins power at the general election.
Party leader Jeremy Corbyn said half of the homes built would be council and housing association homes which would be "for rent and totally affordable".
Labour said figures showed its councils had built more homes than Conservative ones since 2010.
The Conservatives said they had a "clear plan" for affordable housing and Labour's policies were "uncosted".
'For the many'
With six weeks to go before election day, Mr Corbyn reaffirmed his party's housing pledge on a visit to the Conservative-held seat of Harlow, saying: "We want our country properly housed.
"We want our young people growing up with security so they can achieve more in school and college and go on to university, because this election is about the future and removing that sense of insecurity that so many face.
"We are for the many. They are for the few."
Labour councils have built on average 2,577 new homes between 2010 and this year, compared with 1,679 in Conservative-led areas, according to a Labour-commissioned study of House of Commons library analysis.
It showed Liberal Democrat councils performing slightly worse than the Tories, building on average 1,660 new homes.
But challenged over housing at prime minister's questions on Wednesday, Theresa May said that more council housing had been built under the Conservatives than under the last Labour government showing the Conservatives were "delivering on housing and delivering for ordinary working families".
The government says it has measures in place to boost the numbers of affordable homes.
Following Mr Corbyn's comments, Conservative Party Chairman Sir Patrick McLoughlin said: "Yet again, Jeremy Corbyn's uncosted policies demonstrate what's at risk at this election.
"Under Theresa May, we have a clear plan to deliver more affordable housing - and the number of housing starts is up by three-quarters since 2010. But that would all come to an end with Jeremy Corbyn in charge of our Brexit negotiations, bringing grave risk and uncertainty to the British economy."
Labour Housing spokesman John Healey earlier said Labour councils in power were helping people to get that first foot on the property ladder, building super-efficient homes in Exeter and "genuinely affordable" homes in Islington, north London.
Asked whether Labour's approach to house building was through councils, Mr Healey told BBC Radio 4's Today programme: "You have to have councils building and commissioning new homes as part of a much bigger effort from housing associations, private house builders and councils."
Mr Healey, a housing minister in Gordon Brown's government, said that decades of missed housing targets was a "test that all us as politicians have to meet".
"It's no good announcing big figures and targets. People have lost confidence in that.
"We have got to show not just what we want to do, but how we will do it and how we will fund it."
House prices in England and Wales have risen 259% between 1997 and 2016, according to the Office for National Statistics, while average earnings have risen only 68%. Home ownership in England is at its lowest level since 1985, according to the government.
In February, a government White Paper on the state of the housing market in England noted it was "broken" set out plans to build more affordable houses and help people buy and rent.
The housing strategy for England included giving councils powers to pressurise developers to start building on land they own.
Ministers also pledged to make renting more "family friendly" with longer tenancies offered.