Struggling young families have seen their access to social housing fall as fast as their chances of buying a home, according to new analysis of the housing crisis.

The shrinking stock of social housing has seen the share of young families who live in it fall by around a third over the past 20 years, with 400,000 fewer living in council and housing association homes. It comes despite the rising need for low-cost homes.

The latest research, carried out by the Resolution Foundation, highlights another aspect of the intergenerational divide. It found that the decline in social renting by young families has coincided with rising levels of “housing stress”, as the proportion of families spending more than a third of their disposable income on housing costs rises across the population.

About one in 10 low and middle-income families now face housing stress. However, younger families in the bottom half of the income distribution have been hit with the sharpest increases, with one in five households headed by an under 35-year-old being forced to pay what many regard as an unaffordable amount for their home.

The fall in access to home ownership for the young – as a result of rising prices and stagnant wages – has become a major issue for the government, with senior Tories desperate to see purchasing a house become a possibility once again for new families.

The research shows that poorer young families also lack the option of social housing. The share of young people in the bottom half of the income distribution living in social rented accommodation has fallen as fast as home ownership. Both fell by more than 10 percentage points between 1996 and 2016.

This is partly as a result of the Right to Buy policy, which saw those in council houses allowed to buy their home at a discount. It has meant that older occupiers of social housing had access to properties and were helped into home ownership. A depleted stock of social housing has never been replenished, leaving the young increasingly reliant on private rentals that come with high costs and insecure tenancies.

In fact, the research finds that for many young adults their best hope of living in social housing is to stay in their parents’ home, as part of the so-called “boomerang generation”.

The share of social rented households where adult children continue to live with their parents has risen from 5% in 1996 to 7% today; it is now larger than the share of owner-occupied homes where adult children still reside (6%).

There are hopes that a long-term decline in social housing is beginning to turn around. Last year ministers vowed to build more homes for social rent, backed by the promise of £2bn of support.

Lindsay Judge, senior policy analyst at the Resolution Foundation, said: “Britain has a proud history of providing social housing. But the sector has been in decline for decades and is too often ignored in national debates about housing.

“It’s welcome that the government has finally recognised the need for social housing and that we are talking about the sector again after the tragedy of Grenfell last year. But there needs to be a lasting shift that sees Britain’s social housing providers rise to the challenge of providing the homes that so many young families in particular need.”

Prime minister Theresa May has made housing a priority of her domestic agenda, but there are concerns on Tory benches that Brexit has led to a lack of action in other areas.

A government-backed commission has concluded that action is needed to speed up the rate of housebuilding. The review by former cabinet minister Oliver Letwin, to be published tomorrow, finds that thousands more British bricklayers need to be trained to help meet building targets.

It suggests that a shortage of British bricklayers will have a “significant biting constraint” on government plans to boost the number of new homes built from 220,000 a year to 300,000.

It also concludes that housebuilders are limiting the number of newly-built homes released to prevent a glut on the market hitting prices. Letwin says developers could increase the choice of design, size and tenure of new homes without impacting on the local market and therefore speed up the rate at which houses are built and sold.