Millions of young families are entering an era of insecurity in which renting becomes the norm, according to a report that warns of steep increases in the number of parents unable to buy their own homes.

The Cambridge University study, obtained by the Observer, says that if the British economy remains stagnant, just over one in four people – 27% – will be in "mortgaged home ownership" by 2025, compared with 43% in 1993-94 and 35% now.

Most alarmingly, it finds that it is no longer just young, single people who are locked out of the property market and forced into an under-regulated rental sector due to rising house prices, falling real wages and banks that are unwilling to lend.

The same difficulties are now besetting families with children, many of whom are paying half or more of their income in rent and, as a result, have little or nothing left at the end of the month to save for a deposit.

Over the past five years, analysis shows that the number of families with children having to rent private accommodation has soared by 86% – more than double the increase across all households (41%).

The new report, commissioned by the independent Resolution Foundation and the housing and homeless charity Shelter, predicts that this trend away from ownership towards renting will continue apace for more than a decade unless the economy picks up markedly.

The increase in the proportion of families with children who are renting privately will be most stark in London, it says, rising from 25% now to 33% by 2025. Overall, it predicts that more than a third (36%) of British households will be renting by 2025.

"The worse the economy, the more the likelihood of this group's housing being in the private rented sector," the report says. "In London, if current trends continue, tenants will soon outnumber owners, with important political, social and economic implications."

Shelter's chief executive, Campbell Robb, said the study showed government must acknowledge renting is fast becoming a "way of life" for the majority of Britons. He and other experts want the government to do far more to encourage investment in the private rented sector and to protect the rights of those who are unable to buy, after a period of cuts in funding to the social housing sector and as household numbers rise.

Tenants complain of numerous problems in the rental market, in addition to uncertainties over rent levels and the sense that they lack a permanent home. Before a tenancy commences, letting agents and landlords can make a series of discretionary charges – including credit check fees, inventory check fees, tenancy agreement fees, and even unspecified "admin" fees. After moving in, many tenants complain about the time taken to carry out repairs, and the way many landlords fail to give the statutory 24 hours' notice before visiting the property. Many tenants also report problems recovering their deposit in full when they move on.

"This report shows what is fast becoming the new reality of our housing market in the current economic climate: home ownership continuing to fall while renting becomes a way of life for British families," said Robb.

"Yet despite the growing pressure on the rental market, the government's recent housing strategy virtually ignored the sector and did little to address the issues of affordability, stability and quality that so many renters face. It's time government woke up to the fact that 'rental Britain' is here to stay.''

Housing minister Grant Shapps said he did not believe home ownership was in irreversible decline. But he accepted there was a generation of young people, many with children, who were struggling to get a foot on the housing ladder.

"The housing crisis – which has been decades in the making – has led to a crunch situation in which an entire generation is boxed in," he said. As a result, Shapps said, the government had announced a series of measures to help people enter the market and boost the provision of homes.

These included a scheme agreed with the Home Builders Federation and Council of Mortgage Lenders to offer loans of up to 95% of the value of the home on newly built properties in England, to support 100,000 households. The government's housing strategy also involves "build now, pay later" deals for developers, and the release of enough brownfield land to create 100,000 new homes and up to 200,000 new jobs.

Last November, ministers announced a review by the businessman Sir Adrian Montague into how to encourage institutional investors such as pension funds to get more involved in the private rented sector. The report is expected to be delivered to ministers this month.

Many in the industry believe the UK should move to a regime more like Germany's, where tenants have extensive rights including security of tenure, assured rental rates and protection from hardship caused by unfair practices.

Vidhya Alakeson, director of research at the Resolution Foundation, said families who are forced to rent needed security in a regulated market. "With children attached to schools and parents to work, it is critical for households – and for society – that families can find stable and secure rented accommodation to raise their children in."

Stuart Ropke, assistant director of the National Housing Federation, said: "This report highlights the chronic shortage of housing in the UK and the need for a bolder and more ambitious government strategy to increase the supply of new homes across all tenures.

"Although ministers agree that we need around 232,000 new homes annually to meet demand, only 118,000 homes were completed in 2010-11 – little over half the number required to fix our broken housing market.

"We urgently need to get the construction industry moving. Building new homes will help ease our housing crisis and spur economic growth by creating jobs and supporting local businesses."