Homelessness is sadly becoming a reality for increasing numbers of young people, and plans floated yet again by the prime minister and chancellor this week to abolish housing benefit for under-25s will only make things worse.

There is nothing unusual about someone in their early 20s living with mum and dad in 21st-century Britain. Indeed, in laying out his plans to abolish housing benefit for under-25s, chancellor George Osborne said: "There are plenty of people listening to this programme who can't afford to move out of their home, but there are people on benefits who can get housing benefit under the age of 25."

Osborne seems to be talking about those many young people struggling to get on the housing ladder – an issue around which much of the debate on young people and housing focuses. It is not hard to see why that is such a concern: sky-high property prices, the need for a substantial deposits and the growing reliance on the bank of mum and dad mean that for many home ownership is out of reach. But there is another story, less often told, of a growing group of young people falling even further down the pile. What Osborne didn't mention is how precarious things are out there if you are unfortunate enough to be young yet unable to live with your parents.

About 380,000 people aged under 25 are currently supported by housing benefit. Of these, 204,000 are parents (mostly single mothers), at least 66,000 are working, and 28,000 are sick or disabled and claiming ESA. Around a quarter (99,000) are looking for work.

There are many reasons some young people cannot live at home. Their parents may have died. There may not be enough space, or indeed they might have moved away to look for or take up work. They may have suffered abuse at home, or have simply been told they are not welcome to stay or move back in. Latest government statistics show that 10,000 people were accepted as homeless last year because their parents wouldn't or couldn't house them.

It is sometimes suggested that these young people who rely on housing benefit are somehow living a life of Riley. In fact, the situation for many is very precarious, having been particularly badly hit by the government's sustained cuts and changes to housing benefit.

Research for Crisis found that fewer than 2% of properties are now available and affordable for single young people on housing benefit in the private rented sector, despite ministers saying that the cheapest third of properties should be. The lower shared accommodation rate of housing benefit to which those under 35 are restricted just doesn't reflect the reality of rents in much of the country.

This combination of a failing housing market and an inadequate benefit system means that thousands of young people are already being shut out, struggling to find a basic room to rent, never mind a home of their own. Our new campaign at Crisis, launched just before Christmas, is calling on the government to address this by thoroughly reviewing how the shared accommodation rate is calculated so it covers the true cost of renting a room. We of course also continue to call for a massive increase in the number of decent affordable homes being built, which would bring down both rents and the housing benefit bill.

Because make no mistake, this toxic mix of high unemployment, low wages, a lack of housing, high rents and benefit cuts is already taking a terrible toll. The number of under-25s sleeping rough in London has more than doubled in the past three years. A full 8% of under-25s say they have been homeless in the last five years.

And what has been the government's response? To kick off 2014 by proposing to throw fuel on the fire of issues facing young people by considering restricting the ability of those under 25 to claim housing benefit. The experience of similar cuts under the Thatcher government highlights clearly what will happen – thousands will be condemned to a spiral of hostels, night shelters, squats and sheets of cardboard laid out under bridges.

Yet again our politicians are reaching for solutions that hit the weakest, no doubt to raise a cheer among certain sections of the press and public, but ducking the really bold moves, such as pledging to build more homes and provide more opportunities for well-paid work, which would improve lives and communities and really bring down the benefits bill.