The economic downturn and the government's deep cuts to welfare will drive up homelessness over the next few years, raising the spectre of middle class people living on the streets, a major study warns.

The report by the homelessness charity Crisis, seen by the Guardian, says there is a direct link between the downturn and rising homelessness as cuts to services and draconian changes to benefits shred the traditional welfare safety net.

In the 120-page study, co-authored by academics at the University of York and Heriot-Watt University, Crisis highlights figures released over the summer that show councils have reported 44,160 people accepted as homeless and placed in social housing, an increase of 10% on the previous year and the first increase in almost a decade.

Last year another 189,000 people were also placed in temporary accommodation – such as small hotels and B&Bs – to prevent them from becoming homeless, an increase of 14% on the previous year.

Crisis says that with no sign of economic recovery in sight, there are already signs that homelessness is returning to British streets. In London, rough sleeping, the most visible form of homelessness, rose by 8% last year. Strikingly, more than half of the capital's 3,600 rough sleepers are now not British citizens: most are migrants from eastern Europe who cannot find work and, unable to get benefits or return home, are left to fend for themselves on the streets.

The charity says the evidence is that the current recession has seen the poor suffer the most, but other parts of society may be in jeopardy if the government's radical welfare agenda is acted on as the economy stutters.

"Any significant reduction of the welfare safety net in the UK as a result of coalition reforms may, of course, bring the scenario of middle-class homelessness that much closer," the report states.

The charity says that the government needs to reverse cuts to housing benefit and invest urgently in new housing. It also calls on ministers to withdraw the most radical provisions in the localism bill, which would make "temporary accommodation" for needy families just that. Under the new legislation, councils would be forced to remove parents and children who have been in a hotel for a year. At present the assistance is open-ended.

There is also an alarming trend in what the charity calls the "hidden homeless" – families forced to squeeze into one room rather than a flat. It says 630,000 households are now "overcrowded", with London and the south-east the worst hit. This trend could worsen: this summer a survey by the National Landlords Association found more than half of private landlords were planning to reduce the number of properties they let to tenants on housing benefits. Crisis says more families will be forced to share an ever decreasing number of homes.

In a separate report, Channel 4 News will broadcast further evidence that official figures underestimate the true picture of homelessness. In Crawley, West Sussex, the Open House hostel said it turned away people needing a bed almost 2,000 times last year, although official figures estimate there are just seven homeless people in the town. Two-thirds of homelessness organisations nationwide told Channel 4 there had been a rise in rough sleeping in their area.

Leslie Morphy, Crisis's chief executive, said: "We are extremely worried. Homelessness in both its visible and hidden forms is already rising and as the economic downturn causes further increases in unemployment and pressure on households' finances, homelessness is likely to continue to rise. This research is clear that it is the welfare and housing systems in the UK that traditionally have broken the link between unemployment and poverty and homelessness, yet these are now being radically dismantled by the coalition government. The government must listen and change course before this flow of homeless people becomes a flood."

Crisis argues that instead of doubling its efforts to end the "scandal" of homelessness, the government is in effect making it impossible for those on low incomes to pay their rent. It says in the past British welfare policy, unlike that in the US, has linked housing benefit to actual rents. But the government's changes break this link and mean that claimants will be priced out of swaths of the country – or end up on the streets in wealthy regions.

The report also says the government's "affordable" house-building regime is likely to generate fewer than 50,000 homes by 2015, "well short of the 80,000 required to meet ministers' targets". Gone will be the lifetime tenancies offered by councils which had to give priority to those in need. Instead, under new powers, local authorities will be able to choose families with "local connections".

With the coalition's welfare reform bill heading to the Lords and MPs voting on the localism bill next week, Labour said Crisis's warnings were a "timely reminder of a looming homeless catastrophe". Karen Buck, Labour's welfare spokesperson, said the government had played down the rising number of people who thanks to the economic downturn were forced to rely on housing benefit.

She said that since the government took power another 150,000 families had been forced on to housing benefit. "The numbers relying on housing benefit to help with housing costs have been soaring. These figures include not just the unemployed but hundreds of thousands of working families. Rising rents, benefit cuts and housing shortages risk a homeless catastrophe will with all the associated human and financial costs."

The Department for Communities and Local Government said: "Ministers have always made clear their commitment to ensure the most vulnerable in society are protected, which is why the government is investing £400m in preventing homelessness, and has announced plans to extend the London project, No Second Night Out, across the country so no one spends more than one night sleeping rough.

"But the most important thing the government can do to help struggling households to stay in their homes is to keep interest rates low, and to do that we must cut the deficit. That is why we are introducing reforms that will cut the housing benefit bill. But to ensure a smooth transition to this new system, the government is giving councils a £190m fund to help those families most in need.

"Far from the claims made by Crisis, the government's £4.5bn affordable homes programme is set to exceed expectations and deliver up to 170,000 affordable homes by 2015."