More than half of the people living in private rented accommodation say they are struggling to pay for it. A YouGov poll of more than 4,500 people for housing charity Shelter shows that 53% were finding it hard to pay their rent, and a further 3% were falling behind on payments.

The survey reveals that 15% of private renters are worried about paying their rent this month and that nearly a third, 32%, have had to cut back on winter essentials such as heating or clothing to meet their financial obligations.

The figures highlight the extent to which the housing crisis is gripping the private rental sector. Unable to afford homes of their own, tenants are being hit by rising rents as landlords take advantage of the acute shortage of housing. The number of households in private rented accommodation is now similar to that seen in the 1960s, when England’s housing crisis triggered a furore that led to Shelter’s creation. The charity marks its 50th anniversary this year, amid concerns that high rents are pricing key workers out of inner cities and that accommodation for families who have to rent is increasingly inadequate.

Shelter was launched in December 1966 to publicise the housing crisis in Britain’s inner cities. It followed a BBC drama, Cathy Come Home, that depicted the devastating effects of homelessness on one family. A major slum clearance programme led to a large decline in the number of people living in substandard rental properties, but Shelter chief executive Campbell Robb said many of the issues Shelter sought to address half a century ago persist.

“Thankfully, the slums of 1966 are gone, but sadly, despite the progress we’ve made over the years, a housing crisis is once again gripping this country,” said Robb. “Fewer houses are being built, tens of thousands of families are living in temporary accommodation, house prices continue to rise, pushing more people into private renting, and conditions in many rented homes are as bad as we’ve seen in decades.

“These are just some of the consequences of failure by successive governments to address the root cause of these problems by building more genuinely affordable homes and providing adequate support for those who fall on hard times.” Shelter estimates that 250,000 homes a year, half of them “affordable”, need to be built in England if the crisis is to be addressed. However, latest figures show there were only 135,050 new homes over the past year, a rise of 17%, but still little more than half what is needed.

England’s housebuilding programme peaked in 1968, when 352,540 homes were built, and reached its nadir in 2010, with just 106,720. The construction of social housing has declined hugely. It reached a peak in 1993, when 57,020 homes for social rent were built, but had fallen to 9,590 by the last financial year.

The private sector now accounts for the vast majority of new homes, and the proportion of households in private rented homes has almost doubled in a quarter of a century. Some 10% of households were renting privately in 1991, compared with almost 20% now. Last year, the number of households in England in private rented accommodation rose to 4.4 million, a fraction below the 4.5 million high at the start of the 1960s.

Figures released last week suggest that the number of tenants in serious arrears is rising. There were 84,200 tenants more than two months behind with their rent in the third quarter of 2015, the latest figures available, compared with 74,000 in the second quarter.

Government statistics show that the use of bed and breakfast accommodation for homeless families with children is rising. Over the past five years, the number of households living in B&Bs has more than doubled, from 2,050 to 5,270. Meanwhile, the number of homeless households in temporary accommodation has risen by 26% over five years, from 51,350 in 2010 to 64,710 in 2015.

The issue of affordable housing will be a major issue during this year’s London mayoral election. Figures highlighted last week by the Resolution Foundation show that one in four people renting privately in London spend more than half their income on rent. Housing is now the number one issue for Londoners, according to a poll conducted by Ipsos Mori on behalf of London councils.

A spokesman for the Department for Communities and Local Government said the government had a bold and ambitious plan: “We are determined to create a bigger, better private rented sector and are attracting billions of pounds of investment to build homes specifically for private rent, which will increase choice for tenants.”