Overcrowding in social housing has increased to the highest level since government records began 24 years ago with more than 300,000 households in England squeezed into too few rooms, official figures have revealed.

More than a quarter of a million households are also living in overcrowded private rented housing, which is the second highest level recorded since 1996, the English Housing Survey revealed on Thursday. It means at least 1 million people in rented homes are enduring overcrowding.

Increasing numbers of younger people at an age when they are bringing up young families are likely to be affected by the squeeze. The proportion of 35- to 44-year-olds in the private rented sector has more than doubled in the past decade from 13% in 2007-08 to 28% in 2017-18.

Overcrowding rates are now eight times higher in social housing and six times higher in private rented accommodation than among owner-occupiers, who are far more likely to have two or more spare bedrooms.

Ten per cent of homes in the social rented sector were underoccupied compared with 54% of owner-occupied homes, the annual survey of more than 13,000 households in England showed.

The housing charity Shelter, which is running a cross-party campaign fronted by the former Labour leader Ed Miliband and the former Conservative party chair Sayeeda Warsi for 3.1m social houses to be built, said the figures revealed a market “full to bursting”.

“It’s no coincidence that the number of people trapped in expensive and unstable private renting is still incredibly high, while the supply of new social homes has become almost frozen,” said Polly Neate, the chief executive of Shelter.

“The private renting market is full to bursting and that comes with a heavy price tag. From the parents at their wits end bringing up their children in short-term rentals where they can be asked to move at the drop of a hat, to the older, retired renters who live in constant fear of the next rent hike.”

Private rented homes were also more likely to be damp, less likely to have at least one working smoke alarm and were more likely to contain hazards such as infestations and electrical dangers that pose a risk to life, the figures showed.

Fourteen per cent of private rented homes have “category one” hazards, compared with 6% rented from councils or housing associations. Overall, however, the standards of homes are improving. In 2017, a fifth of dwellings failed to meet the government’s decent homes standard, down from just over a third a decade earlier.

Labour’s shadow housing secretary, John Healey, said: “These figures show the impact of Conservative ministers’ mindless cuts to housing investment at a time when new social housing has never been needed more.

“The country is now building 30,000 fewer social rented homes each year than in 2010, while there are over a million households stuck on council waiting lists. Labour would build a million new genuinely affordable homes over 10 years to start to fix the housing crisis.”

The Ministry of Housing, Communities and Local Government said it was “committed to increasing the supply of good quality social housing”.

“We have made £9bn available through the affordable homes programme to March 2022 to deliver 250,000 new affordable homes, including for social rent, and have delivered over 407,000 new affordable homes,” it said.

“By abolishing the housing revenue account borrowing cap at autumn budget, we have set councils free to build council homes for a new generation.”

This week the housing secretary, James Brokenshire, announced nearly £500m to build 11,000 affordable homes in England, plus £9m to crane 78 new homes assembled off site on to the rooftops of buildings in London, with the first appearing by the summer.

“These measures are all part of our plans to deliver 300,000 homes a year by the mid-2020s,” he said.