Young people and families with children are increasingly facing homelessness, according to a study, which says rising numbers of people are finding themselves without a roof over their heads.

The report, from Heriot-Watt University and the University of York, says all forms of homelessness are continuing to rise in England, and argues that "deepening benefit cuts are likely to have a much more dramatic impact on homelessness".

It concludes: "All of the indications are that the expanding risk of homelessness is heavily concentrated … on the poorest and most disadvantaged sections of the community, who lack the financial and/or social 'equity' that enables most people to deal with work or relationship crises without becoming homeless."

The report says national rough sleeper numbers rose by 23% in the year to autumn 2011, from 1,768 to 2,181 – "a more dramatic growth dynamic than anything seen since the 1990s".

The number of families who ask for assistance from authorities because they are about to lose their homes rose from 40,020 in 2009/10 to 50,290 in 2011/12. "This increase in statutory homelessness has disproportionately affected families with children," the report says.

The capping of housing benefits is "generating by far the largest difficulties in central London", it says. "In central London [the effect of capping benefits] will be to drive up the number of 'out-of-area' placements of statutorily homeless families to cheaper parts of the country."

On Monday the Guardian revealed that as cuts reduce the number of properties affordable to people on benefits, more than 20 London local councils had rented properties as far away as Corby, Cornwall, Blackpool and Newcastle to house London families. Councils stress that they attempt to place people "voluntarily".

Elsewhere in England, Wales and Scotland, according to the report, "greater concern focuses on the new 'under-occupation penalty'" – under which the government will cut the amount of housing benefit that people can claim if they are deemed to have a spare bedroom in their council home.

According to the government's own figures, the introduction of the new criteria is likely to cost an estimated 660,000 claimants living in the social sector an average of £728 a year.

The charity Crisis, which commissioned the report, said coalition plans to end housing benefit for under-25s to cut £2bn from the welfare budget would only make matters worse.

Its chief executive, Leslie Morphy, said: "The coalition is sweeping away the safety nets that have traditionally saved people from the horrors of homelessness. Housing benefit, the duties of local councils and the security and availability of social housing are all being cut back.

"Young people are already bearing a disproportionate burden of the cuts and economic downturn, yet the government seems set to increase the pressure by abolishing housing benefit for under-25s. The research is clear: if we carry on like this, rising rates of homelessness will accelerate – a disaster for those directly affected, and bad for us all."

The report notes that instances of individuals and families who become homeless but find a temporary solution by staying with family members or friends, or by squatting – so-called "concealed homelessness" – show "signs of recent increases" after being static for decades. The report says in 2012 there were 1.54m "concealed households". Housing minister Mark Prisk said: "This country has one of the strongest homelessness safety nets in the world, and it is misleading to suggest otherwise. The government has protected £400m funding to tackle homelessness, which is actually lower than for 28 of the last 30 years, and we're reversing the dramatic loss of affordable housing under the previous administration by building 170,000 new affordable homes by 2015."