Danielle Morey, 28, has a problem in common with millions of other voters in Britain today: she can’t afford to buy a home and doesn’t qualify for oversubscribed social housing for which over a million people are waiting. So her only option is to rent privately. In a parallel reality, that is where this story would end. Morey would find a place and settle down with her fiance, young son and 11-month old daughter. Instead, her family has been forced to move nine times in the past decade because of problems such as mould or being evicted through no fault of their own. Her four-year old boy, who is starting school, has already lived in four different homes.

“I am really interested in what the parties say on social housing,” she said. “We have been looking at who to vote for, but it seems hardly anyone is interested in getting younger families into affordable housing, and I mean actually affordable [cheaper than 80% of market rent, which is a common definition of affordable].”

That is why Morey is exactly the kind of voter Jeremy Corbyn wants to attract with Labour’s ambitious proposal to start building 100,000 new council houses a year – up from 6,287, the second-lowest level in peacetime since council house building began in earnest in 1921.

Labour is calculating that renters are now an important constituency and many want reform. The number of families raising children in rented homes has doubled to almost 1.6 million in the last decade, as the possibility of owning recedes. In England, 4.5 million households rent privately – one in five – and conditions are frequently grim. Renters used to struggling with damp, faulty electrics and cold will not be surprised to know that a quarter of the privately let homes are in such disrepair they are classed as “non-decent”.

Landlords also retain powers to evict tenants such as Morey using so-called “no fault” eviction proceedings. Although Labour and the Conservatives have promised reform, such evictions have become a leading cause of homelessness in England, with 27% of households in housing need citing loss of private-sector tenancy as a key factor, according to ONS data.

Research published on Wednesday also showed that private housing is almost completely unaffordable in many areas for people who rely on housing benefit, which has been frozen since 2016. In a third of areas of England, fewer than 10% of homes are within reach, according to a study by the Chartered Institute of Housing and the homelessness charity Crisis. That is forcing increasing numbers into homelessness or emergency and temporary accommodation. Councils spent almost £1.1bn on temporary accommodation for homeless households in the 2018-19 tax year, up 78% over the last five years. There are prizes to be had for politicians who can deliver change.

Labour in particular hopes its housing offer will help it fend off opposition in urban areas, particularly where it is under attack from the Liberal Democrats. In Morey’s constituency, Portsmouth South, a third of households rent privately. It is one of several dozen tight marginals with higher than average numbers of renters, and policies to help that group could swing results. In Kensington, where there were just 20 votes between Labour and the Tories in 2017, 36% of people rent, according to the last census in 2011. A quarter of voters rent in Hastings, a Labour target, and the same number in Reading East, a Conservative target.

According to Toby Lloyd, a housing expert who advised Theresa May on policy in Downing Street, two key voter groups care strongly about renters’ rights and conditions: frustrated younger people who are priced out of buying, and their parents, who are not directly affected but are angered by what they hear about the issue from their grown-up children.

But while the issues matters in some places, housing is not a top-ranking priority for voters nationally. According to a YouGov survey last month, it ranks behind Brexit, health, crime, the economy, the environment and immigration. It is on a par with education and has greater salience for Labour supporters, Londoners and the working class. It is of less interest in the Midlands and among leave voters.

Voters will also have to ask how deliverable Labour’s promise is. As well as 100,000 new council houses a year by 2024, it promises 50,000 new “affordable” homes. If these are added to the current output of private housing, it would require builders to add more than 90,000 homes to the annual output, a surge not seen since the end of the second world war.

Setting aside the need to borrow the £75bn to fund the programme over five years, a Labour government will also need to deal with skill shortages among planners and builders. The most realistic way to achieve the goal would be to simply insist that more of the housing currently being planned is turned over to social landlords.