The formerly homeless are increasingly trapped in homes riddled with damp and infested with rodents after ministers gave councils powers to force those without a roof over their heads into rented accommodation rather than wait for a council house, a report by Britain's biggest housing charities has found.

In the largest investigation of its kind, Shelter and Crisis followed 128 households in three regions of England – east and south-east London, Greater Manchester, and East Sussex – over 19 months.

The charities found that the homeless had been housed in "shocking" conditions often at the mercy of "unresponsive" and at times aggressive landlords who threatened eviction if tenants complained.

Damp and mould were the most frequently mentioned problems by those put into rented accommodation. Rodent and insect infestations were regularly reported – most commonly cockroaches and mice, with some examples of rats. These, the charities said, ranged from seeing a mouse once a day to infestations that made the property uninhabitable.

There were complaints of water running down the walls with surfaces being wet to the touch. In one case water was running into electrical sockets, and another reported their ceiling caving in from a leak that was never fixed.

The most pronounced impacts were on respiratory health. About half of the participants reported an increase in frequency of coughs and colds, as well as more visits to the GP.

One mother told the researchers: "My son, his chest is really bad … They're always developing colds. They're always ill. They're always sick. My little girl [was] never ill. But she's been ill about 15 times in the last year."

People, the report says, struggled with household costs such as energy and food. To manage them they went without food, lighting and heating on a regular basis.

Both Shelter and Crisis say the current welfare regime does not recognise the difficulties of dealing with the rental market. First, they argue, housing benefit covers only rent, leaving no cash for deposits, advances and expensive letting agent fees. Both say councils should offer support for longer than six months to allow for more stable tenancies and call for the government to consider action against rogue landlords.

Campbell Robb, chief executive of Shelter, said: "It's heart-breaking to hear that so many privately renting families who are working hard to get back on their feet are being failed miserably. How can parents hope to give their children a better future when their homes are falling apart, making them ill and forcing them into debt?This report should serve as a wakeup call to the government that private renting isn't working for too many people. Unless we see urgent changes to private renting that give families a stable home where they can put down roots, many of them will continue struggling in vain to build themselves a brighter future."

Housing minister Kris Hopkins said: "Tenants have a right to live in homes that are safe and healthy and over 83 per cent are satisfied with the quality of their accommodation. We are tackling the small minority of rogue landlords – from giving extra funding to councils to tackle beds in sheds, to putting in place a package of measures to improve property conditions. However, we need to get the balance right, as excessive regulation would force up rents and mean less choice for tenants."

On Tuesday official statistics showed a 5% rise in rough sleepers, an indication of more and more households being affected by benefit cuts and a lack of affordable housing. According to the government there were 2,414 people reported by local councils across the country sleeping rough on any one night in 2013, up from 2,309 in 2012 and from 1,768 in 2010.